Sixes, I've used both and can see no difference and there's an equal number of people that favor one over another. I've seen extremely small groups with both.
Winchester is usually a little better then Remington. I would go with Winchester. Its suppose to be a little more consistent all the way around. If you want some good 7mm brass, I think maybe lapua or norma makes some, and I know Nosler makes it. Will agree with 7mmfan though about seeing small groups with both rem and win brass.
I have had good luck with both Rem and Win brass. Some folks look down on Rem brass, but I have never had any issues with it. Both case life and accuracy have been good.
Having said that, I bought some Nosler 280AI brass. Weight sorted and ready to go. I always run new brass through the sizing die to ensure the necks are correct, but it didn't appear that I even needed to do this with the Nosler brass.
So I would recomend you go with Nosler brass.