I suspect your 338 is much like my 375 is on deer. Even the 270 gr bullets do not open fast on a deer, over penetration without fast expansion. Hence, they don't kill as "fast" as a 257Weatherby say.
I shot a 250 pound buck in the neck, facing me, hit him just off center in the muscle. Turned him a flip but he got up and ran. Three running shots later he was down. I believe my 270 would of killed him with that neck shot.
I used to use 200 gr ballistic tips in m y 338 win mag. Sometimes the expansion was dramatic and sometimes not. The buck I referenced took first shot broadside through the lungs and he took off running. 2nd shot entered in front of his right hindquarter and exited in front of his left shoulder. That one REALLY messed him up but he was still trying to get back up so I popped him one more time for good measure. One doe I shot I could literally stick my forearm through her from entrance to exit. Had one of those BT blow up on a buck's shoulder about 15 years ago and I switched to Accubonds and all deer are either DRT or just a couple of leaps and down.
I'm using a 338-06 AI I had built last year more these days for woods hunting. I load it with 200 gr Hornady SST bullets and have only shot a couple with it. I like what I've seen so far. Does not expand too rapidly on entrance but leaves a large wound channel and exit hole. Both deer DRT with barely a quiver. I will also try the 210 partition at some point in this gun.
I used the 300 gr Sierra in the 375 before and its made for big tough game. I've loaded up some 300 gr RN Hornady bullets but haven't had a chance to test them on a deer.