I have used both and have never noticed a difference in the way gun shoots.

What you want to do with different brass is to trim all kinds that you have to the same length.  Then fill each one with water and measure the amount of water in each one.  Quite possibly you will find one manufacture will hold more or less than the others.  The ones that hold more are possibly weaker brass.  So if you are approaching the maximum load for a caliber these brass may seperate before the stronger ones will.  This is all considering that all the brass that you are checking is new or once fired.  After they have been reloaded a few times all bets are off. 

What I usually do is buy the manufacture that has the best price and work up loads from there.   

I use both Winchester and Remington brass because both brands are the most readily available to me where I shop.  I've heard that Remington brass is a bit thicker walled making less volume inside the case.  I have not had a problem with pressure or getting all my power into a remington case.  I've also heard the opposite too.  I think things change slightly over the years between lot numbers and brands.  I've never had a problem with either brand when it comes to brass. 

Only centerfire pistol I reload is 45 ACP

Use both Rem & Win and don't notice any difference.

Both will hold all the powder (at least in those I've used) you would want.

Good to know there isn't that big of a difference. I probably have 75% winchester and 25% remingtion brass for the .270 right now.