Actually, the 7mm RUM is probably the least useful and the most specialized of the Ultra Mags.
The .338 RUM is probably the best matched in terms of capacity to bore diameter. The .300 is useful for those looking for a .300 Magnum, but anything it can do, the .338 can do better, whether it be hunting or long range shooting. The 7mm is very overbore, which typically leads to finicky cartridges that are hard to load accurately for, can show larger standard deviations in velocities, have lower brass and barrel life, ect. While I don't doubt that a 180 gr .284 caliber Berger VLD at the velocities the 7mm RUM could push it at would be an outstanding long range performer, I don't see it beating a 300 gr Sierra out of the .338, at least at any real distance.