Both cartridges are very similar. The PRC has more factory ammunition options, and it has much more support for reloading such as brass and dies. The PRC has also been around a little longer so the Western still could take a little longer to catch on. However, I don't think the 6.8 will ever gain as much popularity as the 6.5 PRC.
Having said all of that, I think of the 6.8 Western as essentially a 6.5 PRC that shoots 20-30gr heavier bullets at very similar velocities. That will provide a little better performance on big game such as elk. I think both are good options and I think ultimately the PRC is the best all around option for most scenarios. With you wanting this to be a backup elk rifle, that would lead me to choose the bigger cartridge, the 6.8 Western.