My MTB partner is an ex-pro MX-er and his son is a lifelong MX-er. My background is strictly asphalt. I used to be able to turn trackday times that would qualify me at the absolute tailend of an AMA grid. I have zero dirtbike experience; never owned one.
What I notice:
A.) Their ability to pick lines. I'm used to that, but, on asphalt, the line criteria is totally different. Dirt you're avoiding ground obstacles, asphalt it's connecting corners.
B.) They're very comfortable with trees and threading them. I'm still working on that.
C.) They weight the pedals like a dirtbike. I'm still working on that.
D.) They push the bicycle down into the corners, like a dirtbike. I'm used to leaning my body to the inside. So, I'm still working on that, too. Grazing trees with my shoulder or CamelBack is really encouraging changing my style.
Their motocross experience really shows on a MTB. Their comfort level is far beyond mine. If only I had been nurtured on a dirtbike. Of course, I don't have the crash scars/issues like they do, either.
Oh yeah, me getting a 29er has erased some of their advantage through the rutted/rooted stuff.