I used a 404 Jeffrey over the course of a month hunting in South Africa and Zimbabwe several years ago.
Using 400 grain A-Frames and Barnes Banded Solids in a Heym Express rifle, it accounted for more than twenty animals, ranging from a 2 lb Genet to a very upset charging Elephant. In between there was an eland, zebras, giraffe, cape buffalo, lioness, bush pig, black-backed jackals, baboons, vervet monkey, kudu, hyena... well, you get the picture.
The A-Frames struck very hard and killed everything very effectively. Chrono'd velocity was 2,350 fps. The 404 Jeffrey started getting referred to as "the hammer of Thor" - that pretty well sums up how it performed.
Backup rifle was a Ruger RSM in 416 Rigby, using 400 grain A-Frames as well. Velocity was 2,400 on the nose. It took a zebra, eland and an impala as well as a baboon.
On a previous safari (in RSA and Zim) I used a 375 H&H in a Ruger RSM (with a Verney Carron double rifle in 450-400 3" NE as the "primary" rifle that stopped working shortly after taking a black wildebeest in RSA).
The Ruger RSM worked like a charm. Most game was taken with .375" 300 grain A-Frames, but three giraffe and a zebra were taken with heavy-for-caliber .375" 380 grain South African "Rhino" bonded heavy partition bullets. These performed "almost like a .40 calibre" in the words of my PH. Later on I saw first-hand what he meant. The .40's, both the Jeffrey and a Rigby, hit hard, putting game down quickly - no messing around. My personal preference would be the 404 Jeffrey.
I would endorse the 404 Jeffrey as a perfectly capable cartridge for any sort of larger game, including stuff that might want to turn you into goo.
Easy to shoot well. Just a nice cartridge. It would be fabulous in a Winchester model 70 with CRF or a CZ 550/Brno 602.