Here in New Zealand we have no big game seasons or limits, so we hunt big game all year round. We have deer ranging from what we call Wapiti (Elk), to the similar body weight Sambar, then slightly smaller Red (known as Stag to you guys I think), then Sika, Rusa, Fallow and even Whitetail.
I have personally shot over 500 head of big game, and guided and witnessed the shooting of thousands more. These range from the biggest Wapiti down to the smallest Fallow, with the majority being Red and Sika deer, at ranges from point blank to 1500 yards.
The bullet I've shot by far the most big game at long range with is the 7mm 180gn thin jacket Berger, and it is a truly exceptional bullet for this job. It has definitely been the quickest killer of game beyond 500 yards, and also the easiest to hit with due to its BC verses velocity potential in the big 7mms. I also really like the 200gn Wildcat terminal performance wise, but I've run out of them! The 162 A-Max and 175 SMK also perform pretty good. This is in generally lightweight rifles, where the 7mm is king, due to the performance vs weight vs recoil tradeoff. In the heavier guns the 338 300gn SMK is an extremely reliable performer, and I expect the 338 Bergers to be even better! (Please Eric!!! I've rethroated most of my reamers to suit them in anticipation so I hope they're not too far away now!?!?!?)
There are exceptions to every rule, but the neither the AB's nor any other controlled expansion bullet will kill as quick at long range as the Bergers, even with Elk sized animals. Its all about impact velocity, there is no such thing as a bullet with ideal terminal performance at both 50 yards and 1000 yards, or nothing of current construction anyway. Yes, if you hit the shoulder knuckle on the largest deer at range, the Berger may not get through, but it will definitely temporarily anchor the animal to allow a follow up kill shot. But an AB through the lungs will allow the animal to travel a long way before it finally bleeds out due to very minimal expansion at long range. It will need to hit the knuckle to achieve much expansion. Don't get me wrong, the AB is my favourite under 400 yard bullet in most rifles, but I run a 2 load setup in most of them. AB's for closer stuff, and Bergers/A-Max's/ SMK's for the longer shots.
The Berger will expand more than a controlled expansion bullet on any shot as a rule, but you will always strike the very odd anomaly if you shoot enough. As always though, this is the exception that proves the rule!
Greg