I would like to hear from everyone on this one...Rick, DB, Rolando if you are still lurking, the real lurker Lurker, Reality, Randy, W.O.W, jn, x3 (where you at!!), sp101, etc
I guess etc. will chime in.

Gregg Popovich (and I've ALWAYS thought this) is spiritually, emotionally, and mentally (in the basketball sense) tied to Tim Duncan. I think around Tim Duncan, a dominant offensive AND defensive player, Pop knows how to get other things to fit in around that. Duncan is a low-post presence, so Pop can take journeyman Bowen and turn him into a three point threat simply by the double teams Duncan draws. Defensively you have perhaps one of the most well-rounded players that has stepped on the court as your anchor. I've never given Popovich FULL props simply because of the sheer dominance of Duncan and Popovich has never done well without Duncan on the floor. Now I admit that I've swayed a little in that, Popovich has impressed me with the development of Tony Parker and Manu Ginobili. We'll, of course, see whether I eat crow when Duncan retires but I just don't see Pop being as comfortable coaching the Dallas team as he is with San An. Even though Nowitzki probably is a more dynamic offensive player than Duncan and even though top to bottom, Dallas has more depth and talent than San Antonio. Depending on whether or not Pop meshes well with Terry and
especially Howard, I see Dallas being a top 4 seed with a real shot at the Finals at best and a 6th, 7th seed first round ouster at worst. Overall a little worst.
Avery Johnson will do well in San Antonio since he acquires a defensively stable team, no need to rip his hair out telling Nowitzki why wandering to the perimeter defensively is not condusive to stopping penetration in the lane. On the other side of the ball, Avery will do well with the likes of Udrih, Finley, and Bowen. You wonder how Duncan takes the shock to the system of a new coach but you'd think Parker and Ginobili would welcome at least a willingness to open the game a little during stretches. Avery could become to happy with this and in the process shift the focus away from Duncan, in which case San Antonio begins to do worst. As long as he keeps Duncan at the forefront and utilizes the deep (albeit aging) roster of San Antonio to exploit mismatches and keep guys fresh, he should do well. At best, one of the top 2 seeds and a championship contendor. At worst, a 5th, 6th seed no one wants to play. Overall no change.
Despite all that, I think it would be an egregious mistake for both teams to switch guys even though I don't think either team will change all that much with the change. Popovich knows the ins and outs of almost every player in San Antonio and has become a master of staying competitive during the season while keeping an aging roster fresh for a long playoff run. Avery Johnson is probably used to the young, youthful thoroughbreds that can run all day in Dallas (Howard, Harris, Daniels (previously), Ager) and might overuse the likes of Horry, Finley, Barry, Duncan, etc.