I'll probably get ripped apart for this comment, but I'm not convinced that "wired is better" as a blanket statement is broadly true - the quality of the headphone likely plays a much larger role.

Back in the early aughts when MP3s became prevalent, some grad school colleagues and I were testing sound quality for different songs across different genres from lossless down to 56 kbps. We had to get a fair bit below 128 kbps to noticeably hear any loss for most songs. So I'm willing to bet that most people, in a double-blinded experiment, cannot identify wireless/wired better than 50% of the time (therefore they're guessing) for good quality headphones. If anyone knows of the results of a double-blinded experiment that proves me wrong I'll happily shut up. Otherwise one of these days I'll have to run the experiment myself.