I've done the UA trip in F and C. The advantage of F is that you can get horizontal, which is a great aid in actually sleeping. This matters for your question because NZ is putting in lie flat seats (the same as those used on Virgin Atlantic, the best in the sky according to some) on its C class for the US-NZ transpac portion. To my mind that seals the deal.

If you plan on using UA award miles for the trip it's impossible so far to get seats on NZ. If you're using $, I think its no contest.