There are many different aspects of the game that could contribute to the 6 stroke difference in handicaps. Lots of aspects can contribute 1-2 strokes at that level:
bag management (having a well chosen set of clubs)
ball management ( choosing the right ball for your game and the course/conditions)
shot inventory (how many different kinds of shots you have available to choose from)
being one club longer off the tee
being a 3% better putter (by # strokes)
being a 20% better pitcher/chipper (by distance to the hole)
There are some who argue that a single handicap is misleading, that one should have handicaps for driving, irons, pitching, chipping, sand shots and putting. Check out Dave Pelz's Short Game Bible!
Despite Mudfoot's experience, it's highly unlikely that there is just one reason for the 6 shot difference. Consistency is the most noticeable, but that can come from many different sources.
You also need to be careful what you're looking at. As a 12 handicap I think I putt as good or better than a scratch golfer if you had us both putting from the same location head to head. But I'm well aware a scratch golfer makes fewer putts per round than I do because their approach shots, pitches and chips are all better than mine.