Would I get better browning with stainless steel?
Not necessarily; the browning mostly depends on the temperature and grease on the pan. Stainless steel pans tend to be thicker than non-stick pans (though there are countless variations), hence they take longer to heat.
What are some general rules about things that are better cooked in stainless vs non stick.
You'll basically want to be extra careful to make sure the food doesn't stick to a stainless steel pan. A trick used in my household is to
Heat the pan until really hot
Turn off the stove
Let the pan cool for a few seconds
Pour in the oil and start frying
Are there certain foods to avoid in stainless (to avoid ruining the pan or scrubbing all day).
I've never encountered a dish that can be fried in a non-stick pan but can't be fried in a stainless steel pan.
Here are the only pros and cons between those two types of pans considered in my household:
Pro: They allow us to cook with less fat.
Con: If food gets stuck (it happens... a lot), scraping the pan detaches tiny bits of that non-stick coating, which could be hazardous to your health.
Stainless steel pans
Pro: They increase the iron content of the food cooked in it. If food sticks on them, some hard scraping wouldn't do anything bad to your health.
Con: They require more oil to avoid sticking.
Believe it or not, we've entirely converted to not using non-stick pans due to that con.