I have shot both and hunted with the Beowulf. I don't know that you could go wrong with either one for your situation.. Both are pretty significant calibers. I would also add .458 Socom to the mix (which I have also shot). Recoil is stout on all three, but nothing terrible by any means.
If you aren't reloading, it looks like .450 Bushmaster has more numerous ammo offerings and slightly cheaper than the other two calibers.
As I don't think you will be able to tell the difference in lethality between the three at those distances, and given the lesser cost for the .450 Bushmaster, I would lean in that direction.
.450 BM will be easier to find (on shelves) no doubt. But the .458 SOCOM has far and away more offerings (types and weights of bullets) commercially loaded than the Bushy. But.....ammo for the bushy is significantly less costly.
Anyone choosing the 50 Beowulf or 458 SOCOM should handload to take advantage of the many different bullets available to keep costs reasonable.
I DO agree that at distances of 150 yds. and less that all three will perform similarly (with like bullet weights and types).
The SOCOM and Beowulf leave the Bushy in the dust when it comes to using heavier bullets (not necessary for Deer or Hogs in most cases).
For economy, reasonable recoil, ammo (off the shelf)....the 450 BM is a good choice. I use the SOCOM but I hand-load. It will shoot anything from a 100 grain bullet (yes 100) up to 600 grains.