First of all, the three are not even in the same ball park. The .500 Phantom (in an AR-15) is a higher pressure round that uses special parts from the WSSM ARs to maintain integrity. It pushes a 300 gr bullet at something like 2500 fps while the Beowulf, at much lower pressures, gets maybe 1700 fps with a 300 gr bullet..
Then there is the .50 BMG. You've obviously never seen one or you wouldn't have to ask... It has a *HUGE* case to hold lots of powder, and propels a 668gr bullet to ~3000 fps.
With any of the three, your range is only limited by your skill... A slow round with a pathetic BC like the .50 Beowulf will make range estimation *critical* past a few hundred yards. Most people lack that skill, never mind being able to deal with the drastic effects of wind on such a bullet. That's why many people consider it only effective to 200-300 yards.