BB has the same issue as the other brands of a multitude of reports of premature stick drift. I have heard great things about the thumb stick tension options.
There are options out there that are better but AFAIK you can't use them with a PS. e.g. there's a Razer model PC players swear by, and there's a controller that has optical thumb sticks (I think that's what they are, I don't have time for a bunch of google-fu to look it up) instead of electronic potentiometers, which can be recalibrated if they develop drift.