I have a custom classic Rigby style M98 express rifle built up in 9.3x66 Sako (aka 370 Mag) that would be very close to the 380 Howell in performance. The rifle is very balanced, reasonably light and trim. Perfect stalking rifle with good range and a bit of grunt.
Comparing her to the 375 H&Hs I've owned, she's a pound lighted, less bulky, holds 5 rounds and quicker at snap shooting and follow-up shots due to the above, along with a shorter action throw. Does she kick? Yes, but the stock is well fitted and I would say felt recoil is no issue, and certainly no more than a std 375 H&H would be.
I'm very pleased with with her and she does everything I ask of her. If shit hit the fan, would I reach for her over a 375 H&H? Yes, primarily due to her packability and deadly speed to put into action. To me, this out weighs a bit more power that the 375 H&H has. I don't think an animal would notice the difference though. Calibre aside, this just goes to show you that the rifle itself plays a very important role in determining which is your "go to" gun.
Yes, ammo availability is a concern if lost. But this has never happened to me yet over three and a half decades hunting. If I'm worried, I'll check two bags and put half in each, so if one is lost or delayed I'm still in the action.
If I was to do it again, would I do it the same? I would build up the exact same rifle, but would only consider the 375 Ruger as a different calibre option. That is something you might want to consider as well.
As such, I have what I have and am very pleased with her.