Bullets that are high sectional density and are moving at moderate speed give the best penetration. Super speed magnums have to shoot very hard bullets with limited expansion and near total weight retention to have deep penetration. Light, fast and tough or heavy, slower and softer are your choices. The Browning BAR in .30-06 with a 200 or 220 grain bullet will work, or get it in .300 Win Mag with a tougher faster bullet such as Barnes TTSX. It should be available in .338 Win Mag as well. The FN FAL can be rebarrelled to .338 Federal I believe. The .338 Federal is supported by Sako in bolt guns, but it is a necked up .308 Win and will fit in M14 or FN FAL magazines or any other .308 Win magazine and action.
It only takes one shot of .375 H&H, if you are a decent shot, to put down anything. Shot placement counts for more than anything. Bigger, slower, heavier bullets like a .338 Win Mag, .375 H&H, 45-70 Govt., .416 Rigby, 9.3x62mm are less affected by deflection off bones than the faster and lighter small caliber bullets. They are usually not found in semi-auto rifles.
Passing up shots where I am not 100% confident of putting a bullet where I want has always worked for me. That is why I now mainly use a 7x57mm Mauser (modern CZ 550, not old surplus rifle) because it goes where I want it to go. Spending a lot of days at prairie dog towns teaches you how far you can shoot accurately, and you can take your big game rifle there as well. I have picked up some fairly heavy brass at prairie dog towns, like .300 Weatherby Magnum, so I am not alone in this belief. Karamojo Bell bird hunted with his rifles. It's all about getting accurate.
You will have a hard time finding a semi-auto rifle that handles more powerful rounds than what a Browning BAR does.
Location, location and location are three main rules for successful business. Practice, practice and practice are three main rules for hunting success. Benchrest accuracy counts for diddly squat under actual field conditions.
