the 308 is a perfectly good sheep rifle for a few reasons...

1) it works better with lighter bullets as relative to the 30-06 (which does better with the big-boys).
2) sheep aren't that big
3) short actions are lighter... and going after sheep is a bit of an adventure to say the least
4) easy to get ammo.

now, I wouldn't go out an buy a 308 JUST FOR SHEEP... but if you've got one, use it!

to me, a sheep gun would be 270WCF, 270 WSM(blah), 257wby, or 7mm-08.

270 for its ballistics and reasonable recoil
270WSM, ballistics AND lighter rifle... but crappy ammo availability and $$$$
257wby just to reach out and touch someone at 500 yards!
7mm-08, light rifle, light recoil, 7mm ballistics.