The stainless you pretty much never have to worry about, unless you leave an empty pan on a very hot burner (which I've done, and even then the steel survived but is discolored). The tin you can get too hot and melt, and it does wear out over time.
That being said, tin is a much better conductor of heat than is stainless. So, the response time from a stainless lined pan will be slower than a tin lined one. I think I've also read that tin is very good at food release.
If you are getting a sauce pan or something that will always be used with a liquid in it (except for deep frying in oil, not sure about that), then a tin lined pan makes sense, as the water will keep the pan at 212 degrees. If you are going to be searing or something like that, I wouldn't go for tin, too easy to get the pan too hot and ruin the lining. Real copper lovers turn their noses up at stainless, but each has its pro's and con's.