"...suitable for anything from coyotes to moose..." So is the .308, .270, .280, etc, etc.
Ballistically, the .30-06 and .308 are identical. Using the same Remington factory 165 grain Premier AccuTip bullet, there's 78fps difference and 105 ft-lbs of energy at 500 yards, in favour of the .30-06, and the case length. The '06 can use a 20 grain heavier max bullet weight(220 vs 200), but that really means nothing. Both give the best accuracy using 165 grain hunting bullets and/or 168 or 175 grain match bullets.
"...the .308 has about 20% less recoil..." That's nonsense.
The .308 lets you use a shorter action. If that matters to you.