They are both 30-caliber. Since the .30-30 is loaded to a lesser pressure than most other "really" modern cartridges--being shot in the older lever actions--The performance is not such-a-much.
Basically, the common .30-30 load shoots a 170-grain bullet at 2,200 ft/sec muzzle velocity; the AK round shoots a 1390-grain bullet at around 2,300 ft/sec.
"Best" is a function of your intentions with the rifle. Beaucoup variables--hunting, home defense, plinking, target...And, rifle styles within these--bolt action, single shot, semi-auto, lever action.
If you're talking the typical deer-hunting use, other than at fairly close range, they are marginal to minimum. It's not that they won't kill; the issue is a quick, clean kill, or anchoring an animal in the event of a bad hit.
Hope this helps, Art