I have the 458 socom. It shoot .458 bullets. The 450 uses 452 pistol bullets (same as 45 colt 454 casull). That is a plus for the 450 because these AR rounds are all in the same class as magnum pistol rounds. On paper (wiki) the socom is slight more power than the other two. The 50 Beowulf is obviously the largest bore. I think two top out just under 3000 ft-lbs energy (2800). The socom tops out at 3300ft-lbs on wiki for first place edge. I like 458 socom cartridge design with a shoulder to head space. And, I like the 458 bullet selection.

I would say the three are about the same, because there is only so much you can fit into and AR15. The real difference, IMHO, turns out is the bullets. Brass is easy to find for all three, if you go online. The 450 probably has the bullet availability edge (pistol bullets). Socom in 2nd place for bullet choices. Unless you want subsonic blockbusters. The socom has the hvy bullet edge. Or suppressed, the socom. The 50 has the big-bore braging rights edge and probably least selection of the most expensive bullets. I have on occasion seem loaded 450 ammo on LGS shelves, never the other two. That was fair priced Hornady 450 ammo.

If you consider reliable feeding with good hunting performance, there is probably a very limited selection of good polymer tip bullets for any of these rounds.

The 450 seems like the only one of the three that does not have some kind of license or proprietary issues. No voodoo secrets. Given a choice of Alexander 500 or rock river 458, I choose RRA. Easy choice for me. I image the 450 is available on a wider range of platforms and easier to build with proper spec parts.

Edit: I may be mistaken on the 450 bushmaster status. Quote from wiki:
Quote
The .450 Bushmaster is a rifle cartridge developed by Tim LeGendre of LeMag Firearms, and licensed to Bushmaster Firearms International.


This would make all there big boys a pain in the proprietary butt.