.303 Savage (not British!) internal ballistics are very slightly better than the 30-30.
Due to the model 99's magazine arrangement, .303 Savage can be loaded with more ballistically efficient spitzer bullets which would give it an additional advantage at longer range. I'm unaware of what's currently available as far as factory loads, the advantage may be only theoretical unless you handload.
None of that is enough to take it out of the 30-30 class of cartridges.
With a well placed shot at reasonably close range it'll kill an elk, but I think that there are better cartridges out there for the job.