Off the top of my head, the advantages of the 300 RUM would be if you already have a LA Rem 700 you want to use and since you said you are single feeding it would work fine in a 300RUM build without going to a custom action with the larger super mag .588 bolt face and the RUM has tiny advantage over the straight 300 Lapua. ADG makes great 300RUM brass so I don't see any brass advantage for either.
Personally, I would never do a straight 30-338 Lapua or 30-338 Norma. If I didn't want to fireform and "improve" the Lapua or Norma I would stick with the 300RUM. BUT, if you are ok fireforming and you want to sling the 250's I would head straight to the 30-338 Lapua Improved. Improving the 338 Lapua case has a pretty healthy amount of pick up over the none improved version.
I have one of Kirby Allen's 300AX which is his version of a 30-338 Lapua Improved with 35° shoulder. I'm sure some will gasp but mine is actually built on a chromoly LA Rem 700 and wears a Lilja #6 finished at 28 less brake. Mine was built a number of years ago when the heaviest available bullets were the Berger 230's so mine is a 10tw, not sure I can shoot the 250's. I have a Seekins det mag setup in my build, don't think Seekins makes the one I have anymore, that allows a max OAL of 3.900 and if I recall I'm seating the Berger 230 Hybrid Target 3.850. I'm sending them at 3250fps which is a full load but nowhere near redline. I've pushed those 230's as hard as 3400 testing max pressure but that was definitely redline+. In my gun 3250 w/230's is it's happy place. I will say, it has been one of the easiest to load for and most forgiving rifles I've ever owned.
FWIW, if you're considering a 30-338 Lapua Improved you may want to talk to Defensive Edge Rifles. Shawn builds quite a few 300 Terminators, that's his version of a 30-338 Lapua Improved, and he even has dies and already formed brass available for purchase.
As for case design and which one is inherently more accurate, talking to someone like Alex Wheeler or some of the others on this forum would probably be much more beneficial to you.