The real issue here is what are you planning to hunt? Big Bitie Stuff needs low power, fast response, big FOV. Most DG scopes start at 1 power, and hover around 1.25-1.5. My Swarovski Dangerous Game Reticle choice was 1-8 the dg reticle is circle dot. Fast and efficient. Love it. On the budget end the Leupold 1.0 or 1.5 -5 are great choices on the VX5HD line. Oddly - my longest South Africa Hunt shot is 475 yds with a Sako Safari model in 375 H&H on a Blue Wildebeest. One shot, over and done - with the Swaro 0.75-6 Z8. My PH and the crew thought I had lost my mind taking that animal at that range. 2 days later - same model scope on my 416 Rigby on a big zebra at 425. No problem - one shot. 'Doo doo' happens fast in the bush - this is not like what we know as western or plains hunting. Clarity and field of view are serious requirements - especially if the something you're on can bite back.
I never lacked for mag power in Africa on the 375. My 338 WM, on the other hand, had a Swaro 2-12. I typically used that from the battery on lighter game and potentially farther shots. Worked out great. Frankly - I can't imagine running a 4x anything as the starting power in Africa. You've got to find the animal quickly - and probably on the run.