The new military Special Purpose Rifles and Squad Advanced Marksman rifles - both in 5.56, are getting ranges of 600-800 yards, and scoring kills on man-size targets. The SPR is using a high power scope, while the SAM-R is using a 4x ACOG. That said, the energy drop is high and the .308 maintains far greater energy at those ranges, as well, as noted, with less wind drift, but it still is not known as a stellar long-range performer. You need a bullet with a high ballistic coeficient to get really stellar performance at range.
I'd decide on the kind of ranges I expect to be shooting, and then pick a caliber accordingly.