I've owned my .308 since 1971 and its taken game from moose to mule deer. Very accurate and plenty of power. In contrast, I owned a 30-06 briefly and found the excessive recoil too much for me and sold it. I'm no fan of recoil.
I can load 200 grain Speer bullets in my .308 but velocity suffers. But I discovered that Nosler Partition 180's shoot flatter and penetrate deeply. So these Premium 180's are my favorite for truley big animals.
The hunter with a 30-06 rifle can shoot heavy 220 grain bullets. This may be considered an advantage by some. But I'm not convinced I'll ever need to shoot 220 grain bullets.
30-06 has been proven as a reliable big game cartridge wherever game is hunted. It's been around for over 100 years.
.308 has been proven as a reliable big game cartridge wherever game is hunted. It's been around for over 50 years.
Fire up the grill! Deer hunting IS NOT catch and release.