Having personal experiance I choose 270gr tsx for 375 H&H and 180gr Accubonds for 300 WM.
Coincidentally, my .300 Weatherby shoots 180 gr and 168 gr TSX bullets equally well. For some reason, and I can't remember what, I have only hunted with the 168s. Blackbuck to elk, four animals, four shots, and four times I tracked the bullet in one side of the animal then out his other side which resulted in four quick kills. Why should I hunt with any other bullet?
I have had very good accuracy with the 150 gr TTSX in my 300 WSM. Also it kills well Good penetration, usually goes completely through. After my experiences from my first safari I suggest NOT using Berger bullets.
Gillettehunter, you better keep the long range specialist on TV from reading your comments on Berger Bullets (lol). Honestly, I think the Berger bullets are just a fancy sales pitch, they are not any better than most bullets on the market. Like they say on TV, they are very long bullets compared to others. To me, there are better bullets on the market....TTSX probably being the best.
I'm a big fan of the swift Scrocco bullet, I've taken 10 or so African animals and this bullet did a great job of one shot kills.
Try a good premium bullet at a sensible velocity most already mentioned here. Then test your loads till its the most accurate it can be. then prtice till you know exactly what your rifle will do under a veriaty of situations. Follow this up with much hunting! There are no better bullets than are being produced right now.
I dunno what is best, but in a 7-08 we've used 140 accubonds for deer for a few years and love them, the deer don't.
My son and I leave in 2 weeks for SA, we'll be carrying the 7-08 with the 140 accubonds and a new 300 wsm in 180 gr accubonds.