Wavebird has a larger stick movement radius, but the wired controller has faster teching and whatever...
Where did you hear that? I thought that WaveBirds were identical to the wired controllers with the exception of the removed rumble pack and the additional components for the wireless elements (it was manufactured by Nintendo so I don't understand why it would be different). What do you mean by "easier teching"? Different triggers?
You should use a wired controller if you have the choice, though either will ultimately be usable. There are still problems with WaveBirds that don't exist with wired controllers:
• They can interfere with each other if someone else happens to use one (which is rare), so you should really be checking with any other users beforehand to make sure you're using different frequencies.
• They can be interfered with by other sources which are beyond your control.
• They don't have rumble (if you care about that).
• They require batteries.
• They're significantly more expensive.
• People have said they have significant input lag (though I don't know whether that's true or not).