I've used 150 and 165 gr. Partitions exclusively for about 40 years, but out of more powerful guns than yours; 30-06, 300H&H and 300Wby.
I started with the 150s because I was hunting mostly deer in the beginning, and shot a couple of elk and one moose with them, all at close range.
Then the day came when I took a shot that I shouldn't have. Don't have any real good idea how far it was, but I had time to get the scope back on it before the bullet hit. The bullet hit dead center just behind the shoulder, and I saw the moisture spray out and around the point of impact, and heard the solid "whump" of a hit. It was pouring rain and a half hour voyage to where he stood. All there was was the odd small drop or blood from the entry wound. To make a long story shorter we gave up when we lost the trail in dog hair second growth over solid moss about a foot deep about 3 hours later.
I switched to 165 gr. Partitions at that time, and it's been bang flop every time since, but it was the same with 150s before that bad day
So I guess it's a judgment call, but given the tiny loss in a flat trajectory I'd stick with 165s any day.
Some may say "go with 180s", but out of a 308 you'll never realize the full performance of Partitions of that weight. Remember too, that if the game is close enough and you hit it right almost any bullet will do the trick.