Stuff like better graphics, better Tesselation and small details?

I think it would be very rare to have an actual agreement to put more effort into the marketed version, or gimp the competition, but I'm sure the people at the publisher would be embarrassed if their marketing partners version would suffer. So some would stay embarrassed, and others might interfere and tell the devs what to do.

I'm talking in terms of consoles, but it's more open and accepted in the PC space wher nVidia offers PhysX, AMD offers Tressfx etc...

Yes. Though it's often irrelevant what's different and how big the difference is. it's just important that it is somewhere mentioned that it is better on a certain platform.

To a certain extent, yea