in the NFL it's more about people/personality management than x's and o's. in college, hc's can be a lot more hands on, and let the staff manage the personalities. the HC is "dad".
it takes two different personality types imo. you typically wouldn't see a DB coach get a HC gig in college. but in the NFL Mike Tomlin can go from DB coach to SB winning head coach, simply because of how he manages people and personalities.
it's how Pete Caroll ultimately made the transition from USC to Seattle.....
there are exceptions obviously....but to me, that's the biggest difference.