Definitely my favorite cartridge and rifles to shoot and hunt with. I've got 3: 2 Model 95 Chilean Mauser Sporters in regular 7x57, and a Model 1909 Peruvian Sporter in 7x57 Ackley Improved. I haven't started loading for the Ackley yet, but I've been hunting with one of the Chilenos for quite a while now.
Power vs Recoil, a 7x57 shot out of a 24" barreled rifle has to be one of the best combinations out there. Regular 140 grn loads don't kick hardly at all, and it will do pretty much anything a .270 can. This makes for a very good rifle for a youth, woman, or small framed person such as myself. I'll shoot belted mags if I have to, but I've never liked the way they knock my 135lbs around, especially shooting offhand. The 7mm bullets are usually very aerodynamically efficient and have good sectional densities.
In my experience, for ranges less than 300 yds, it's the best whitetail deer cartridge out there. Everytime I have used it, it killed quickly and cleanly, without the excess damage to the meat you often see from '06 and .270 velocities. They are reportedly very effective on Elk and Moose as well, but I've never used them on such. As you said, they also work very well on hogs, coyotes, bobcats, and pretty much anything else that moves and needs to be killed.
For disadvantages, ammo availability is about the only one I can think of. It's better than most of the other European rounds out there, but off the shelf ammo is still pretty pricey. Prvi Partizan and Sellier and Bellot are both imported at very reasonable prices however, and I have found both to work very well in my rifles. Brass and bullets are very easy to find, and there's still a lot of boxes of hunting ammo out there floating around used for cheap prices. Keep in mind that anything loaded in the U.S. will be at a lower pressure level. SAAMI limits the cartridge to 51,000psi, while the European rounds are capped by C.I.P. maxes of 56,500psi. The American loadings are in deference to the Remington Rolling Blocks and Small Ring Mausers that were imported in large numbers here. While the small ring isn't necessarily a weak action by design, it's gas handling capabilities are poor, and the metallurgy of the times was very primitive. With a strong M98 or modern action such as a Ruger 77, you can easily load the cartridge up in the 60,000psi range. Then it becomes more of a .280 Remington than a 7mm-08. The 7x57 AI is pretty much the equal of the .270 or .280 when loaded to these pressures. My advice if you have a small ring, enjoy it for what it is, and don't try and hot rod it. The rifle is likely over 100 years old, and possibly a combat vet. It's earned it's life of leisure killing critters.
As far as the Africa big game thing, it was much more a story of necessity than choice. Many of the early African settlers carried Mausers in 7x57. They used them from everything to hunting to dangerous game defense because that's what they had available. Much like the early blackpowder winchesters and muzzleloaders used on the American frontier, they are no longer considered an ideal hunting round due to advancements in technology and hunting ethics. However, at the time it was all they had, so they made do. There's a big difference between hunting for survival and hunting for sport. The reason they are no longer legal for DG in Africa is because countries there have set bore and energy minimum requirements. The 7x57 doesn't come close to approaching either of these at any level of loading. It's not safe for dangerous game, but it has killed it in the hands of good riflemen who had no other choice. The preferred method for killing elephants was a solid bullet shot through the brain. I say preferred, but it's pretty much the only way you're going to even phase an elephant with a 7x57.
For the American hunter that doesn't have a habit of going after big bears, it'll do anything you ever need it to do inside of 300 yards. If you're a bit of an eccentric or that guy who just likes oddball calibers, it's definitely the thing to have.
