Since Rust is still an Early access game, it could have many random problems. Also, as you said, it's not a problem with other games, so it must be the problem with the games. And as I said before, Rust is an Early-A game, so some problems when changing OSes are expected.
But first, is your computer set on performance mode? If it's not, your PC in general will not perform in its full capacity. Enable that first, and it's maybe going to solve your problem.
And for the last piece of advice, update your GPU drivers, or reinstall them. It really might help.
Hope my advice helps!
NeutronPCXT