The Logitech is your best bet. If you disable vibration, batteries will last for ~250 hours or so.
However, know that the d-pad is a bit oversensitive at first (but as time goes on, you break it in and it works as good as any other d-pad). On top of this, the pressure sensitivity for circle/x/square/triangle is not as good as the Dual Shock 2. Play a game like Metal Gear Solid 3 and you'll instantly see what I'm talking about. It's harder to keep your gun drawn and you just start firing, even if you didn't intend to.
That said, it's still the best wireless controller for the PS2.