Here's a good article on the 9.3x62 in case you haven't already read it.
http://93x62mmmauser.blogspot.com/
My son has a CZ 550 in 375 H&H. He loves it and so do I. Recoil, to me, is not as punishing as my .338 Win Mag, and the rifle is extremely accurate.
If you are looking for a real stopper for dangerous game, according to the article the 9.3x62 is it. Apparently the 375 H&H took over the title of the most used rifle in Africa, not because it is better, but due to other factors such as war and politics. According to what I read, Professional Hunters say the 9.3 anchors game better.
As to an all-around big game cartridge, well, apparently the 6.3 is more than enough. Don't let that discourage you, however, if you want to hunt deer-sized animals. My thoughts are what's the point in owning such a rifle if a guy can't use it, or maybe only use it once or twice in a lifetime on an African safari. My thoughts are go with what you like. Have fun with it, do some reviews and maybe load some rounds that will achieve the results you are looking for. Owing and shooting a fine rifle has it's own rewards.
My son took a whitetail deer with his 375 purely for the enjoyment of hunting with it. I have taken deer with a variety of calibers, from 6x45 all the way up through most common cartridges to my 338 Win Mag and 35 Whelen, the latter two again being just for the joy of it. Some may say using those larger cartridges for deer is overkill, and they would be right in the strictest sense in that you don't need such a rifle for deer. But truth is you don't need a 30-06 for one either, so you get my point.
Either way, the CZ 550 platform is a very good one for such a cartridge.