I use both, and prefer one kind over the other only when it's needed for the recipe. Stainless cookware (and I prefer tri-ply or clad, heavy duty pans) is great for sautéing when I want to make a sauce out of the little caramelized bits on the bottom of the pan, or transfer the entire pan to the oven to finish cooking the food. It's also my favorite for saucepans because I feel like I can stir and whisk in the pan without worrying about destroying a non-stick surface.
Non-stick cookware (skillets really) are what I grab when I'm doing a quick saute or browning, making grilled cheese, crisping garlic or pan-frying my dumplings. I prefer ceramic-coated nonstick, but have no problem with PTFE the traditional coating. However, once there are scratches on my non-stick pans I quickly replace them and suggest you do the same.