IANAL: I would assume it depends on the situation. If I move from company A to B, and I own a database in both, it is reasonable to expect that mistakes I made at A I won't repeat at B.

If A and B were pharmaceuticals and I know A secretly wasted 20b on a compound that B is considering to test, maybe this is a trade secret that I should be careful divulging.

My intuition is that there is a line between "taking professional skills with you" and "trade secret".