I think the importance of one over another is not as much a concern in a rifle not used for dangerous game.

For myself the controlled feed on a DG rifle is a requirement not a option. I own and love my push feeds some of my favorite rifles are built on REM actions (my personal favorite rifle is a REM 40X action I had built in .308) but for me a push feed in any caliber from .375H&H and above is a deal breaker, I wont look twice at the rifle for any price.
It may very well never be a issue for most but be assured when things do go bad its yet one more weak link in the chain in a already deteriorating situation and when the chips are down you need all on your side you can muster IMO.

James F. Nixon III