If you were to choose between Norma and RWS brass. Price aside. In 375 H&H and 9.3x62.
Which and why?

Both are exc. I would go RWS, a bit harder & thicker. It lasts along time.

I have heard Norma is very uniform though it is a bit soft and primer pockets get loose fairly quickly, even with normal pressures. So you get less reloads per case.

That's what I found when loading for my .338x74K. It's made up on 9.3x74R. When using Norma, I get 4-5 laods before head seps. start to show up. When using RWS, I am at 7 w/o any signs. I like Lapua a lot too, & they make it in 9.3x62!
http://www.eabco.com/Lapua01.html

I used both in several calibers (6,5x54 / 7x64 / 9,3x62 etc) and I agree with Fredj338 and Allen Bosely, RWS it's a bit harder & thicker than NORMA. For this reason it's possible to reload more times RWAS cases.
Hector

Generally I would agree I absolutely love RWS the best but not in the 9.3x62!

The brass in the case neck is razor thin (I presume it is 30-06 necked up by RWS?) and will not hold onto a bullet well enough IMHO in such a calibre.

I have no knowledge of Norma in this cal - LAPUA 9.3x62 is superlative and likely cheaper to boot!