A capo might make a slight difference in tone. (I disagree with some of the earlier posts).
I did a comparison among three capos, on a higher end, all solid wood acoustic guitar:
- Planet Waves NS Pro (from the pre-D'Addario days)
- D'Addario Planes Waves NS Pro Plus
- G7th Performance 3
The PW Pro and the G7th have a firm rubber band. They result in brighter, crisiper sound.
The D'Addario Pro Plus, by design, has a thicker and softer pad that aims to emulate the barring finger's flesh. This results in a somewhat more dampened sound.
The difference is subtle, but is there.
I have also found other folks on YouTube come to the same conclusion, and also one video where G7th's representative claims that the rubber's firmness has the said effect on the tone.
It's not the capo quality per se—as you asked in your question—that affects the tone (all these three are great quality products), but the deliberate design choices made by the manufacturer. One tone is not necessarily better than the other, it's up to you to decide which one you prefer, among many other properties of the capo.