This is one of those religious debates. It's largely personal in my opinion.
I'm pretty deep in 556 rifles, so for me, I'd go with 556 for ammo commonality. If I was deep in 762, I'd go that route. But conversely, I've heard people argue the opposite in case one caliber or the other becomes hard to find.
762 has better barrier penetration and deeper penetration for hunting inside common hunting ranges we get here in the Southeast. Supposedly this is why GIGN adopted the BREN 2 in 7.62x39.
556 has better terminal performance against mid-size game and two-legged targets assuming you engage inside the optimal parameters for the round you are using.
Some people complain about the proprietary 762 mags. But you supposedly can do a conversion to use regular AK mags. However the proprietary mags give you the benefit of a bolt hold open on last round.
556 can use commonly available mags already.
There are a lot of pros and cons to either way.
Maybe, get both?