Either bullet will work well. They are both no frills deer bullets. My daughter just killed a deer with a .243 and 100 grain Sierra Pro Hunters at 200 yards. I have killed deer and antelope with the interlock in 30-06 The loads worked well. Dead deer and antelope. Good exit. Use the bullets that are designed for deer. Both of those are. Good luck.
ETA. My current go to bullet in my 30-06 and 30-30 are Speer Hot Cors. I am also working up a load in my Blackout with Speer Hot Cor bullets as a purpose build for mountain lions over hounds. I just like that type of bullet.
I have seen the Sierra game king bullets separate from the jackets. That doesn't seem to be the issue as much with spitzer style bullets. The SST bullets also seem to expand a bit much for my liking.