It's a completely different barrel, and a completely different caliber ...
What did you think would happen, your scope would keep the zero for both?
Doesnt matter the gun or who made the barrel, the zero is not gonna be the same. Maybe we need to get a bit more realistic in your expectations ... Swap the scope from two different gun and you'll see a similar result, even if they are the same kind. Change the bullet and watch it change again.
Hate to break it to you, you'll have to rezero, change bullet weight with your 308 and you'd have to rezero forget about caliber. It's not some magic system that keeps the zero across all barrels or calibers.
Here is another clue, hang a suppressor on it and it will change again, change muzzle brakes it will also happen with that. You're taking stuff that used to cost extra time and money with a trip to the smith and doing it at home. Get over it and move on.