I'm related to a few WW2 and Korean War vets. My dad had several older friends that were WW2 vets.
The 7.62X51 ball ammo (FMJ military type ammo) is equivalent in velocity/bullet weight) to the military ammo used during WW2 and Korea.
A few years ago, one of my wife's uncles was talking to me after church one night. We were out in front of the church on a cold wet and windy winter night and I guess Korea sort of came back to him.
He asked me if the M1 Garand was 30.06 and I told him it was. He nodded and said that he thought it was, but he didn't remember for sure. He said there were only two things he remembered about his M1. "It was heavy and it killed good, it killed real good." And then that far off look in his eyes faded and we went back to talking about the weather and the bus driver who'd cut the corner too close and dropped the rear tires into the ditch, blocking exit from the parking lot (the reason we were standing there talking instead of going home.)
FMJ may not expand. But it's a big bullet traveling at a decent velocity.
I use soft points for deer hunting, mostly because it's a legal requirement. I have no doubt, with the bullet placement I had from my M1A on the deer I killed, that FMJ would have dropped them, too. Spine, neck, liver/lungs shots are a real drop right there and die hit.
Some of the Marines, the ones that still hunted after their Island Campaign ordeals, came home and bought 30.06 deer rifles, and carried them till they got so old they stopped hunting. Again, they deer hunted (and some bear hunted as well) used soft point hunting ammo but their confidence in the round came from combat in the Pacific Islands with FMJ ammo and M1 Garands (not saying some of them might have, for a short time, carried M1 Carbines, but when they preferred the power/effects of the bigger/faster 30.06 bullets).
My .308 ammo (M1A and DPMS GII) is a combination of SA surplus (FMJ), S&B surplus (FMJ), and reloads (FMJ).
As they say, your mileage may vary, but FMJ 7.62X51 is good to go for me.