Does heat distribution vary between uncoated stainless steel pans and non-stick pans?
Non-stick pans have a coating on top of metal, this metal could be aluminum, stainless steel, copper, or any  other metal or alloy. The coating doesn't make a whole lot of difference to the heat distribution, that is the property of the metal underneath it. 

Heat distribution doesn't change the end quality of your food, it determines how quickly heat spreads through the metal of the pan. What determines the quality of your end result is your technique in using the combined properties of your heat source and your equipment to cook food well. You can make great food with the most basic of equipment if you know how. 

The type of range you have should have a big influence on your pan choice. I cook on gas which produces a nice, steady heat which I can control very finely, I prefer using a set of inexpensive non-stick aluminum pans as they are light and heat up quickly. I can keep the pan at a steady heat by adjusting the flow of gas. If I (god forbid) had an electric stove I would opt for stainless steel or cast-iron instead because these materials even out the fluctuations in heat from the on-again-off-again nature of electric heating elements.