RE: 375 H&H OR RUM?
375 Ultra is a better performer on paper for all counts.
I jumped from a 375HH to 416 Rigby and haven't tried the 375 Ultra. I'm fairly recoil INsensitive; however, as a good rule of thumb if you are moving up from a 375HH, then be sure to buckle your chin strap.
More later,
EKM