Overwatch is much more team based while in tf2 you can sorta get away with a wacky team since there are just simply more players per team.
TF2 has started to feel more and more F2P as the years have gone on. Let me explain. While a game can be F2P, it doesn't necessarily have to FEEL F2P. You don't have to keep adding more and more items that you can only earn by paying money or simply lock off content from people that give stat changes.
TF2 is full of that now. While Overwatch also has micro transactions there is no "You NEED this weapon to rocket jump". Everything is just a skin and since skins are nothing but cosmetics they are simply up to personal taste. I frankly have never felt the need to go after a single skin, while in TF2 I have multiple times felt the need to pay for a new weapon.
There is honestly a lot more, but it's better to just play the games yourself and get a sense of difference for yourself. Everything between the two games will be subjective between everyone. I could say the movement in Overwatch is better, but you might like the movement better in TF2, etc etc.