Wow! This has gone to the second page without anyone making vitriolic pronouncements. I'd say that times really do change.
Differences? From personal experience, I'd say that the 30-06 was a better starting place for me as a reloader. It may be insignificant, but my first loads with the '06 were perfect the first time out. I had to go through multiple iterations with my first 308 WIN before I found one that would group properly.
I will also say that the recoil tables don't tell the whole story of the differences between the two. If you look them up in most tables, the 308 WIN has less recoil with the same bullet. However, that's assuming the rifle weight remains constant. In reality, the 308 WIN is fired from a short action, which normally weighs less. For a big guy like me, it's no big deal. However, with a younger shooter, it can be a problem. Both my sons graduated from 30-30 WIN to 30-06 for deer rifles and preferred '06 over 308 WIN. KYHillChick also shoots a 30-06.
