30-06 = long action, more powder, more velocity...
308 = short action, less powder, less velocity, less recoil...
308 is so popular for long range competition because its the "Chevy 350" of the shooting world. Parts are cheap, quality load info is easily attainable, mil surplus brass is cheap, mil surplus ammo is cheap, and did I mention the military uses them?

There's quite a few people out there shooting 30-06 in long range rifle competitions, and the caliber really shines when you handload for it, or even go with an Ackley verson... You can build the bigger calibers off the long action (300 winmag, 7 WSM, and other magnum calibers), while you can't off the 308 short action (but you can load some sweet short action calibers too like the 6.5x47 lapua, 243, or any other version of a 6.5/6 mm caliber).
Velocity has VERY little to do with accuracy. Sure you don't have to dial in as much scope adjustment, but with as long as the bullet is staying super-sonic at the range and has an equal ballistic Coefficient value as a flatter caliber, it will be just as accurate provided all other factors equal...
Michael