Skeetlee--
In a way, UBR isn't the best game for an unlimited score gun. It does, though, have the advantage of being the only *centerfire* score competition that has an unlimited class, so...
The only advantage to using an unlimited I can think of (but there may be more) is that you can shoot a chambering that wold be hard to manage with a 13.5 pound bag gun. Esp., if it is a larger caliber. Were IBS to allow an unlimited, I'd use a .338 in a smallish case in a minute, as an experiment.
Since that caliber is not allowed in UBR, the only other advantage is with a heavy, high-BC bullet. And as someone who's fired a 187-grain .30 bullet in a 300 yard group match (unlimited), I can attest that a high-BC bullet doesn't compensate for mistakes in reading the wind. It is a very slight edge, and only there if the bullets as as good as the conventional point-blank bullets.
Edit:
Since I had to fix a typo: An interesting .338 for point-blank score in a heavy rifle -- 25+ pounds -- would be the .338 Federal, made on the .308 case.
If you wanted a bit more -- say, if the .300 grain hybrids proved most accurate -- the .30-06 case would work, or the 7.65x55 Swiss -- essentially a .338/284. I'd want a bit heavier rifle, thought.
Just as a note, I shot a 5-shot .100 group, indoors at 100 yards, with the then-new 300-gain Bergers. These had thin jackets, not the thicker jacket for the tactical bullets offered now. This from a 17-pound rifle with a brake, in a .338-Lapua-sized case. A fair bit of luck, in that this is a hard round to control, and I, for one, couldn't keep it up. But a case half that size, in a 50-pound rifle, wouldn't be bad. It makes a big hole, and so far, I've measured 600 of the .338 Berger Hybrids & they are every bit as good as anything except maybe the original Jef Fowler 66-grainers (when he'd tell you he got in a good lot of jackets...).