Oh boy is this a good question - and the answer isn't always as simple as it might seem (and I'll also state for the record that I didn't totally work this out for myself, thanks Carroll Smith).
Believe it or not, tyre width (by itself) doesn't affect grip. Grip is a result of the friction coefficient of the tyre tread and the downforce applied to it. If you put 1kg load on a tyre and it took 1 kilo of force to push it sideways, then if you put 2kg on it'd take 2 kg of force to move it side ways. Another tyre might take 1.5kg to push a 1kg load sideways, due to stickier tread. On a related note, you can also look at it like this (about the downforce). If you double the tyre contact patch (double tyre width for example) then each square cm (or square inch for people who don't use the metric system primarily, and for the record I'm one of them) will only have half as much downforce/load on it. So effectively, the grip stays the same.
Now as a tread is compacted/squeezed from heavier and heavier loads hysterisis will mean that even with teh same tread, the friction co-efficient actually decreases. But it's only a very relatively small amount. So in other words, if you have a way too small tyre with way too much load, it'll start to lose grip (aside from other factors that also affect it) . So you can't go too small.
Additionally, even though the grip would be the same, if you ran a small tyre, it could overheat the tread, and then it would lose grip big time, so you can't go too small either. Or another way of putting it is this - if a tyre manufacturer produces two tyres in the same tread/model, but one is way wider than the other, then the narrow one would be more easily overheated, so they have to run a harder compound. A larger/wider tyre won't overheat as easily, so they can run a softer compound. And related to that, the larger tyre has more tread (in total volume/mass) so for the same compound as a narrow tyre, it would take much longer to wear out. So, again, they can run a softer (with better grip) tread compound on the larger tyre and still get acceptable tyre life.
So in a nutshell - the wider tyres only grip better, because generally the manufacturers can use softer rubber compouds with better grip, not because of the width all by itself.
With that general topic understood, it can then be clearly seen that 'size' isn't the key factor here - it's tread compound. So if you had two tyres by the same company, one in 175/60 13 that used a certain tread compound, but on the 185/60 13 they changed up to a softer compound then that is the one to go for. But if the 175/60 13 has the same tread compound as the 185/60 13, then the grip would be the same, so go for the cheaper one (and I made those sizes up just for an example).
Furthermore, you've also got to look at what those general tyre size ranges might go onto what cars normally. what you can sometimes find, for example, is that 14 inch tyres are more common on older family sized cars, so the tread compound would be harder on them (possibly) than for the tyres in 13 inch sizes that were made for smaller lighter cars. In other words, occasionally the 14s are a step backward.
Since it's all about tread compound (or mostly it is) then the next thing should also become obvious - a particular size won't matter much, what is really important is that different manufacturers and different model tyres from teh same manufacturers come in a big variety of tread compounds. Some are softer and grippier and some are harder and long wearing. So two different tyres - both the same size - well one can be downright dangerous, and another can grip so well it is unbelievable.
So basically you really need to look at specific brands, and specific models of tyre from each brand. Some of the really cheap tyres out of china these days (and there's also some very good tyres coming out of there as manufacturers are moving production to wherever they can for cheaper labour) grip surprisingly well. In the dry at least. In the wet some are satisfactory, but generally for good wet grip, you aren't going to find it in a cheap tyre.
OK - so as far as tyre choice goes, mostly it's a case of asking everyone you can about each brand/model and working out which suits your needs. If you don't need to get long life out of them, you can really get some great tyres (not cheap, but that's the way it goes). If you do, then you have to compromise and find the combination of grip vs long life that fits the best.
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Aside from that, there's also profile - or tyre sidewall height. These days with bigger and bigger wheels out there, people are running ultra low profile tyres. For a few reasons. First of all would be running a 19-20 inch rim with big sidewalls wouldn't fit under most cars so they have to go lower. second reason (probably the first reason if most people were asked about it) is that it has that 'race car' look. I'm not criticising that, it's everyone's choice to do what they want with their car. But they don't necessarily represent the 'best' option.
The flipside of the coin is if you run really small wheel/tyre diameters, or you run really wide (with the wheel offset moving further outward, or spacers or whatever to mount it) - well aside from maybe needing flared guards, either of these two options (eventually) worsen the scrub radius to the point the steering is 'twitchy' over bumps and less stable/less optimal through corners. So if you go really wide, try not to make it a really wide offset (of course increasing 'track' can add stability, so again, it's a compromise - better scrub radius, or better track width, how much of each etc.
It's ok on a racetrack, with low profile tyres, and low ride height, and a relatively smooth surface. That 'works'. It should be mentioned that race tyres often have softer sidewalls, so the sidewall 1 inch high might flex more than a street tyre nearly twice the sidewall height. race tyres also are made to work with lower pressures which produces more flex too. (also - on street radial tyres, don't run massively lower pressure, they won't grip better, they need some stability. About the only thing lower pressures do for street tyres is they tend to heat the tread up more. This can only be a very short term advantage, for something like a hill climb competition where the quicker you get some heat into the tyres the better. But it isn't better for the street (and not for drag racing either). Most street tyres are made to work well with normal heat ranges too, so going hotter isn't a good thing all the time either, even in those small cases I just mentioned that it might work.
But now, on the street, with many bumps and uneven surface, well a taller sidewall has more ability to flex and the actual result is that it can grip better (and improve ride comfort at the same time) than tyres that are too low profile. Not to mention how easy it is to damage rims with the 'rubber band' ultra low profile tyres.
If you go to a taller overall wheel/tyre (even if the sidewall height is the same, for example but one is on a 14 inch rim and one on a 12 or 13) - well that alters the scrub radius, and in a 'good' direction. Can help with stability and generally better mid corner. Problem is, it also raises the car up a little higher, which is worse for body roll, centre of gravity etc. You can of course lower the suspension, but eventually you get to the point that the lower control arm angle with the ground is wrong, So like everything else, it is a balancing act/compromise - finding the best combination that doesn't have too many bad points.
Very generally, the taller sidewall (and it's not really 'tall', like something out of teh 1950s just not the ultra low profile stuff), that sidewall flex helps cushion impact and help grip on uneven surfaces/normal streets - but that extra flex also has to be considered. Remember the early important point - if a particular tyre gets 1kg downforce and takes 1kg to push sideways (which would be a friction coefficient of 1.0) then with 2kg downforce, 2k to push sideways - well the other hidden thing is that to get all of this grip to actually happen, we have to do everything we can to get all the weight of the car being transferred down through the tyre, through the middle of the tread where it contacts the road. We do this by suspension design, and also by adjusting camber and caster, so that the angle of the tyre helps make this weight transfer centred on the contact patch. Since the sidewall flexes more on a tyre with taller sidewall, the car can 'roll over' on the tread and the weight transfer wouldn't be ideal. So to get it 'right' you'd need (compared to an ultra low profile) a little more negative camber (and a little more positive caster) to get the most out of it.
I actually was exposed to this about 20 years ago, but I didn't totally understand it before I came across 'tune to win' by carroll smith (which is still a fantastic book. yes, tyre technology and shock absorber technology has advanced since then, but the general principles still apply) - anyway the 'real world' experience I had was with early toranas (locally made car). I'd ran tyres including 205/60 13 and even tried 235/50 13 which weren't as good (I think it was bf goodrich brand on the 235s) . then I got a set of wheels and tyres cheap, as they only had about 50% tread left. They were 'tiny' 185/60 13 - in yokohama A008 (which were pretty advanced for that time - around 1990/91 approx). Well these 'tiny' tyres absolutely killed the others for grip.
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So after all that - the short version:
- tread compound is important so find the brands with the right tread compound for your needs.
- check the 13 inch range vs the 14 inch range as the 14s are sometimes a harder tread to give ok life on larger cars
- don't go too low with the profile.
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If you wanted some specifics - it really depends on the budget but at the 'top end' of what you could technically call 'street tyres' which would actually work quite well in hillclimbs (not better than a purpose made slick, but better than family car tyres and similar) or days where a racetrack is open for people to run their cars : (and I'm not saying anyone has to buy from this place specifcally, especially if you are outside Australia! I just used it because it happens to have pictures of the tyres in question, but just for the record, they are a decent place to deal with and are popular with a few people I know of who run various competition cars... Not datsuns, but racers are racers!)
the dunlop d93j
http://www.stuckey.com.au/tyres_details.aspx?TyreName=D93Jtoyo fm9r
http://www.stuckey.com.au/tyres_details.aspx?TyreName=FM9Rtoyo ra1 proxy
http://www.stuckey.com.au/tyres_details.aspx?TyreName=RA1make no mistake, these tyres would be lucky to last 10,000km of normal driving, and a lot less if driven hard. But if it is the best grip for 'street racing' (and I'm not saying anyone should race on the street, but just for the sake of discussion) that'd still be legal, and have 'some' tread on it etc - well these ones are worth a look.
If these are too expensive, then there is another option. This option is used a lot by racers in categories where they have to run street tyres, or even more difficult, they have to run a specific brand/model of tyres. for example - HQ racers - which run a control tyre - I thnk Kumho powermax - it has changed over the years as they run varying sponsorship deals. Anyway - they get the tyres 'buffed' which is where they put the wheel/tyre on a sort of lathe and machine away the tread. The taller the tread 'blocks' the more they can move around and squirm, so cutting them short (almost to the stage there is no tread, well not quite - they can't move around and so the grip and consistency is improved _a lot_. The other weird thing - they actually last longer (under the hardest race conditions, not during normal driving) like that. The reason is that at maximum load/cornering, with a full tread, it can start to tear chunks off unevenly, that damages the tread and also causes it to start to slip, and that tears even more of the tread.. So you could get a bit more grip from a cheaper tyre like that, but it means you won't have much tread/safety if it rains, and in most places the tread has to be deep enough to be legal for street driving.
Transfer
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