The debate has faded when it comes to wired vs wireless, it is no longer “what is better?” as it is “what should I use?”. Honestly what I hear the most is “why are we not using wireless?”
I still feel if I can get away with a wired microphone, that is what I go for. If the person is not walking around, and the wire is not a trip hazard, I see no reason to go wired. Although there is less chance of interference today vs ten years ago, I still feel like it is simply more reliable.
So what sounds better. I did a comparison video with 2 different types of the same microphone: Shure sm58. This microphone is a staple of the audio/video industry and you can find at least one around any studio. When you watch this still keep in mind, this is what is sounds like in my camera (Panasonic HPX250) on auto mode with no post done on the audio. Processors make a big difference so just because it sounds like this on my camera, doesn’t be you won’t find a difference on another camera or soundboard. Another big thing is with wireless you have to have a receiver so it may sound different depending on the receiver you are using as well.