I don't own a 7mm Allen mag, but based on the difference in MV and downrange ballistics, the 7mm Allen mag will continue to perform well on large game like elk out to 1500 yds, where the 7mm Rem Mag pukes out at around 1000 yd on expansion velocity. You need to shoot heavy bullets in the 7mm Allen mag to obtain the full ballistic and kinetic advantages. You probably need to have a 10 lb or heavier rifle (bare rifle weight) in the Allen mag to handle the additional stresses strains on the barrel and still obtain sufficient accuracy to deliver out to the ranges it's able to cleanly harvest big game. There's been a shortage of suitable bullets for the 7mm Allen mag but now that Wildcat Bullets is manufacturing custom heavy for caliber bullets, that issue may be taken care of in the not too distant future. Others that own the 7mm AM will likely sound in. There is no comparison between the 7mm Rem Mag and 7mm AM. The 7mm AM is the dragster. The 7mm Rem Mag is a stock car.
If you plan to shoot a lot, the 7 AM will eat barrels much faster than a 7 Rem Mag. But if you feel the need for speed, change out barrels like Nascar changes out tires, and you're off to the races again.
Oh yeah; you won't be buying 7mm AM cartridges at the local gun shop, so plan on reloading with the heavy for caliber bullets - like 200 grain bullets. Your Browning A-bolt is a pip-squeak, comparatively speaking. But I have cleanly harvested game out to 850 yds with my 7mm Rem Mags.