I would guess that with the same bullet weights, the GMM would probably shoot better, based upon my experience, if the rifle has no preference for bullet weight.
Sorry for not providing a simple answer, but it is a complex question and for two manufacturers, two bullet weights and two different rifles, the only good answer will come from shooting them both to see. The difference in 5-round group size at 100 yards may be on the order of 0.020 to 0.050 with the same rifle if you generally shoot 5-round groups that are under 0.4-inchs. It your average group size is over 0.6 inches, your 'shooter induced variation" could mask any differences with bullet weight, especially as close as 7 grains (4 %).
Unfortunately, you really have two questions embedded in one.
Is there a difference in accuracy between two bullet weights in a particular rifle.
Is there a difference in accuracy between two different manufacturer's ammo in a particular rifle.
The answer is probably "some difference" to both and in both, but for different reasons.
Rifle barrels tend to shoot with different accuracy depending upon bullet weight.
In my experience, bullet weight preference varies depending upon the particular rifle barrel. Some rifles don't seem to notice, others are pretty sensitive.
I have two .308s, both Savages, both with 24-inch barrels.
One shoots slightly better with 155gr bullets, the other shoots slightly better with 175 grain bullets.
They shoot with about the same accuracy with 168 grain bullets.
Only each of your .308 rifles can tell you what bullet weight it prefers and it is probable that they won't have the same preferences.
I have also experienced a measurable difference in accuracy between the same manufacturer's factory ammo with different bullet weights.
The muzzle velocity will be different between them, the seating depth might be different, and the amount of bullet body touching the rifling will be different - all factors that can impact accuracy, but a particular rifle's barrel will probably impact accuracy the most.
As for different manufacturer's ammos in the same bullet weight, it also depends.
I have found that Federal GMM ammos shoot better than most Winchester or Remington factory ammos in any caliber that I have tried, especially the GMMs with the Sierra SMK bullets. In fact, Federal GMM with SMK bullets is the first factory ammo I shoot in any new rifle if it is available in the rifle's caliber, mainly because of their consistency over time.
Nosler also makes .308 factory ammo using their Nosler CC bullets and I find it is accurate.
Federal GMM also loads Nosler CC bullets in marked boxes, and there might be a slight difference in results between the GMMs with SMKs and GMMs with Nosler CCs caused by a rifle's preference for a particular bullet.
Although the .308 SMKs and Nosler CCs look almost identical, there might be a slight difference in the length of the bullet body touching the rifling and that might change the accuracy a bit.
Federal GMM may shoot slightly better or worse than Black Hills factory ammos in the same bullet weight, even with the same bullets (Black Hills loads SMK bullets also). Many claim that they shoot the same, others claim GMMs shoot better and some claim Black Hills shoots better. The differences in performance reported may be the result of what powder that either manufacturer used for a particular ammo run or the rifle barrel the shooter uses.
I like both Federal GMM and Black Hills, but I tend to choose Federal GMM as the gold standard for factory ammos, especially for .308 and .223 bolt actions.