I have done it both ways - there are clearly some males that don't care where they are or what they are breeding - others I find do better wallowing in their own filth and I mean that litterally.

I don't think I've come across one that bred better in the females tub (or perhaps it's that I haven't come across a female reluctant to breed in a males tub?) - so for the most part I've stuck with moving females.

Also I think a lot of people keep their males in smaller tubs so it's not space-wise practical to move the females in there.