I don't have or use a .338.

The .375 H&H would be a much better cartridge to use on buffalo. It will do virtually everything the .338 will do with normal ammo ie the 225 gr plus weight range. If you wanted one rifle to hunt all big game with wherever you go in Australia or the world the .375 will do it.

I have used mine on cape buffalo, but no water buffalo. I have used the slightly less powerful 9.3x74R on a dozen or so water buffalo so not much difference. If is devastating on pigs and other medium game. It has similar trajectory to a .30-06 so can be used on reasonably longer shots too. Some guys like to use .375 bullets designed for the lever action .375 Winchester on pigs and no doubt these would kill them very well and are cheap cannon fodder. Recoil of a .375 H&H is brisk but is not too bad, especially if one avoids too much bench shooting.

A .338 Win Mag is IMO a great all round medium game rifle. The calibre range of 8mm to .338 I think is ideal as a world trophy rifle for medium game, from goats and pigs, deer, to the larger antelopes, moose etc. For big game I have no doubt with GOOD bullet placement and good well constructed bullets water buffalo can be killed with it. Starting with the 250 gr projectiles and above. Lots of Aussies use .308s etc for water buffalo seeing there is no legal minimum calibre requirement. Personally I do think a bit more grunt is needed than a .308/.30-06 for the occasions when it is needed. But it is not a stopping calibre. It is also not legal for cape buffalo in Africa should you ever want to do that. Recoil would be marginally less than a .375. From my 'armchair' I have always thought a .338 one of the best all round choices for North American hunting. A .338 would also make a handy sambar rifle and brush rifle.

I was only shooting my 9.3mm with 286 gr SPs at about 2170 fps so a .338 might be able to do similar with 270 gr projectiles. However I did pick the shots on water buffalo and scrub bull going for heart shots trying to avoid the shoulder on the way in.

The old .318 Westley Richards was regarded by many old African hunters as a great plains game cartridge and including use on cape buffalo. The .318 was effectively a .338/06, but .330 calibre on a .30-06 sized case shooting usually round nose 250 gr FMJs and SPs.

My choice would be to get a .375 H&H and use 200 gr to 270 gr projectiles for the smaller stuff, and 300 grs for the likes of buffalo etc.

Regarding ammo .375 H&H would be more common especially for heavier bullets (ie 300 gr) and suitable ammo for water buffalo. You might find some premium ammo in 250 gr for a .338 which will do the work. In the end you will have to reload to feed these beasts economically if you intend to do a fair amount of hunting eg lots of pig hunting.

However if the .338 is your preference seeing your stated intended uses it would also be an acceptable alternative if that is what you decide on.

Have fun.