That's pretty much the argument for the 5.56X45 NATO vs. the 7.62X39 Russky: The recoil is much ‘lighter’, allowing for more ammo on target in a given time. But the M-16 is NOT a machine-gun and shouldn't be used that way for more than a couple seconds. (Ditto for the AK.) That's what a SAW (etc.) is for. Aimed fire (or semi-aimed, in a pinch) is what you want from an assault weapon, and effective ammo is vital. The 5.56x45 ain't it. Not all 7.62X39 is, either, due to poor terminal ballistics, but the larger-diameter round still has the advantage.
That said, even with aimed, slow fire, the M-16 is a much more accurate weapon than the AK-47. The Kalashnikov (that's with an ‘a’, Gunny!) barrel is cheap steel and thus, as you can see in the slow-speed video, flexes horribly when fired. You need bigger bullets from an AK because they strike wide.
Given a choice, I'd take a modern M-14 (NOT M-16) variant in 6mm caliber or larger. The standard for that platform is 7.62x51 NATO (equivalent to a .308 Winchester and thus more effective than the 7.62ComBloc), but 6.5mm (e.g., the Creedmoor or the Lapua) is plenty — and plenty accurate, too. As for price, well, no one beats former commies for bulk, surplus ammo with highly corrosive powder and dubious terminal ballistics. You do get what you pay for!