forget about $ savings when comparing the two. Any savings is burned up in powder, bullets, primers and gas....
To answer one question, my 338 RUM started out as a 338 WinMag. (Rem 700)
The biggest difference between the RUM and Lapua is the brass. The Lapua brass is a bit more expensive but is so much better than any other brass brand that it pays for itself in case life very quickly.
Most extreme long range shooter, me in particular, milk every bit of velocity out of the cartridge, to the point of being obsessive.
This is where Lapua brass shines.
Hand loaded the 338 Lapua is capable of superb velocities along with accuracy.
Hand loaded the 338 RUM pretty much keeps up with 338 Lapua factory velocities. Hand loaded the Lapua almost reaches a different class.
I shot the 300 grain Berger a little over 2700 which seems quite authoritative out around 1200 yards.
A 225 NAB at over 3000 out of the RUM seems all a fella would need. But I'm one of those bigger is better fellas.