The 400-350 load uses the 310 grain bullet and is capable of killing any bull available so long as a solid bullet is used combined with correct shot placement.
If a situation develops where that load is not up to the task then I doubt that any 375 H&H load is going to be all that much better.
As others have said the cartridge is not really a "stopper" when big bulls are involved at close quarters when less than ideal bullet placement ocurrs.
Nor is a 375.
Close range "stopping" is only achieved with a brain shot and the 400-350 with 310 gn solid can easily achieve total brain destruction and instant kill.
Anyone who thinks that a 500 grain bullet in the chest of a charging bull at 10 feet is better than a 310 grain solid in the brain is in for some serious pain sooner or later.

That said, I usually don't back up clients with any less than 45 cal and 500 grains bullet weight and these being solids as well.
The main reason being that most bulls don't charge when wounded but actually often run away and if I am required to shoot I'm looking for shitloads of penetration and bone breaking energy which is easily achieved with big cal solids.

But if I was needing to follow up on a wounded bull in heavy cover, and I had the choice of an ill fitting 500 cal boltgun, or my 400-350-310 double which is a perfect fit, give me that 400-350 anyday!