Seeing as it the hesitation has carried through the carb swap you may want to start checking the distributor and associated components (vacuum advance etc).

To me it sounds like the accelerator pump within the carb is set a little too heavy so that it is over-dosing the engine when you suddenly press the pedal. This pump is designed to squirt an additional supply to the engine when the accelerator is suddenly pressed (to provide enough fuel for the sudden increase). I'm not sure what carb you have but you can normally adjust the setting on the pump so that it gives a lighter dose instead of dowsing the air-fuel mix ratio and causing the engine to splutter.