My favorite powder for the .375 H&H is H4350. I use 76.0 grains behind a 350 grain Barnes Original RN for 2400fps. This is a great load in my rifle with great velocity with good pressure.
My favorite in the .416 Rigby is RX 25. I am using 105.0 grs behind a 410 Woodleigh Weldcore for 2400fps. I have some loads with 110-112 grs that are in the 2600fps range. However, I don't recommend those loads without thoroghly testing lower loads.
I also recommend AA3100, Rx 22, IMR 7828 and H1000 in the .416 Rigby too. These powders all work well but the Rx25 gives noticeably less shart recoil. Probably due to the slower burning rate and low pressure that just pushes longer and not sharper....????
Both of these cartridges are great shooters and have PLENTY of power for anything. Great Shooting. The Bearman