As chappy mentioned, the difference in the stronger partition design shows up more with faster cartridges. One of the beauties of the .308 is that "standard" bullets do a pretty god job most of the time.
You may or may not find your rifle shoots the partition bullets as well. If it does, you would expect similar performance from the partition compared to what you're used to in deer and black bear, no noticeable practical difference really. You will usually get slightly better penetration in moose. You will not notice an advantage on a broadside lung shot, but may on rear angling shots or if the humerus/scapula joint is hit. I personally choose the partition for hunting moose and elk with my .308 rifles because of that very slight theoretical advantage on bigger critters. If you're only switching to satisfy your friend, that's not a very good reason. If you hunt moose more than deer and bears, it might be worth a try.