The pool will always stay the same, regardless which miner you use. It doesn't matter if it is an Antminer S1, S2, S3 or any other miner.
That's not always entirely true. There are situations where some equipment performs below expectation on different pools for various reasons.
My Bitfury rigs hate mining on Eligius. They don't get anywhere the hashrate that they do on BTCGuild. Previously, KNC rigs did poorly on Eligius so they had a special port that they recommended you use. Although I think that was corrected. And doesn't some current hardware have problems on P2pool?
But generally yes, the pool you choose usually doesn't matter.