The US or Team West far better SSBNs
Seconded for this alone, but toss in the bomber force, some of which would survive and get through, and the likely impossibility of getting even most of the ICBMs, much less all, and yeah NATO comes out ahead, the US in particular. The Soviet Navy lacked the ability to track NATO boats to the same degree that NATO navies could track the Soviet boats, the Soviets had relatively few (and inferior) bombers, but they had more ICBMs, so getting all of them was unlikely in the extreme, and for that matter it appears that the Soviets planned a bastion strategy (in the White Sea) for their boats so getting all of them would have been extremely difficult (at least).
In my view, there was no successful First Strike strategy that does not result in both sides being wrecked, perhaps for all time.