There are a lot of good bullets out there. Barnes and Hammers are great for working up close and far out.
Last year I shot a deer with a 151gn Absolute Hunter in 308Win 22in barrel, 260 yards. Diagonal exit. Muzzle velocity was 3000fps +/-10. Impact around 2350fps. Performance was perfect. I mention the Absolute Hunter because it can give you an extra 100fps because of its special design. They are fairly easy to develop loads for, if one is careful.
Personally, with a 308 I would want to be within 400 yards and getting closer. An elk is a large animal and the 308 doesn't have much energy to spare out at 350+, should a more marginal impact take place. But knowing your rifle and how it shoots is the most important. The Absolute Hammer will expand out to 500 yards, if you can put it solidly in the vitals.