My fear would be that an HP would expand too rapidly before reaching vitals on that type heavy game. Of course, better jacket technology greatly increases weight retention on today's rifle ammo.
Best bet would have been a Barnes or A-Square, but I understand the time factor...so going with what you can get is what you have to do in this case.
All that being said, I would chose BOTH.
Load the .50 with a good heavy bullet and pound him with the first shot, and have the .308 on immediate standby for a follow-up if necessary.