To the original question...I wouldn't do either personally.
You'd be better off to build a 6.5 or 7mm or some sort. If your donor is a long action id personally go 260 rem with lots of latitude for COAL. If a short action id go 7mm-08 all day and twice on Sunday. You could of course do a 280 Rem on the long action but imho a 260 or a 7mm-08 will shoot circles around anything built off the 06 case.
If your dead set on a 30-06 or a 8x57...get a 30-06. 8mm bullets suck and the gas tank on the 8x57 isn't big enough to push the 196-200 grain bullets fast enough. Id note the 8x57 shooting 200s is a pretty stout recoiling package as well. But again...I would do either one.
Note that a 8x57 and 30-06 are about equal in terms of HUNTING performance. Id take either one anywhere and do anything with them as far as game taking capability goes. But id rather a 7mm
