Several different ways to look at this:
1) Subsonic transition - what distance does the bullet go subsonic, which is the effective limit of accurate fire? Roughly 450-550 yards for x39 and perhaps 600-800 yards for various 5.56 loads.
2) What's the distance where the bullet retains a useful amount of energy or momentum? x39 will be slightly greater than most 5.56 loads, but only slightly.
3) What range can you realistically hit something with factory ammo? Typical x39 ammo has low to middling accuracy. 5.56 ranges from middling to fairly good (Black Hills Mk262 for example). 5.56 also has a much, much flatter trajectory which makes distance estimation less critical. I would say that beyond 100 yards I expect the shooter using a typical 5.56 load to shoot more accurately than someone with a typical x39 load. (Now, if comparing best handloads with expert shooters, the difference might be very small.)
4) What is the overall platform accuracy? This isn't really apples to apples, but if you compare a quality 5.56 AR to a typical x39 AK, the AR will generally be somewhat more accurate. Though not necessarily as much as you would think, especially if comparing a good AK like a Saiga.
If you want greater range in an AR15, I would look at 6.5G and 6.8 SPC in that order. Possibly also 6x45 and 6.5 MPC. The 300BLK would also have some benefit over both 5.56 and x39 on the retained energy side, but not on the trajectory side (and definitely not compared to 6.5 Grendel or 6.8 SPC).