I'm a 5 to 6 handicapper who drives the ball about 240 on average. Given those choices, I'd go for the 6600, with the 6300 being a little too short. That assumes, though, that the course is not set up as a strategic challenge, with narrow fairways and trouble in the landing zone, or all carry to the greens.
As others have said, it depends on the slope and rating. You can figure your average round as being your course handicap plus the rating plus 3 strokes, and a few more if you don't know the course. If that gets up past 84 or 85 for me, I'd be wondering if I should lower my expectations.
Given several plays of a course, though, I go by the adage that you should play the middle tees until you've broken 80, then you can start playing further back.