First, a reversed polarity is not when you switch out the left and right channels (that’s reversed channels). A reversed polarity is when you wired the + and – incorrectly, like swapping the red and black wires on a speaker set up.
The most obvious effect of a reversed polarity wiring is on the soundstage image. Things that are supposed to play in the center of the soundstage image (that’s right in front of your forehead) instead is like split into two and now playing on the left and right edges of the soundstage image.
Do this for illustration purposes: take both of your hands and put it in front of your forehead. With a correct polarity (and a good heapdhone and a good recording), a certain singer or instrument would be projected there right in front of your forehead.Now, spread your two hands apart to the left and right. This is how an incorrect polarity would sound. The instrument or the singer is no longer in the center, but rather split and is now playing on the left and right edge of the soundstage image.
Other effects of a reversed polarity may include a shift in the frequency balance. You may get more treble, less midrange and such. Of course this may be give the impression that the headphone is now better (i.e with more treble comes more apparent detail), but the fact is that the soundstage image is plain wrong.The best recording to evaluate this phenomenon would be a good live recording. A one instrument live recording like live piano solos would be even better since you have no distraction from the other instruments.