I've tried a number of bluetooth headphones, none of them have had the sound quality of wired. Songs would skip, quality was not great. Are there bluetooth headphones that don't skip nowadays?
Yes. I am extremely happy with the beats solo 2 wireless. No surprise, that they are working well with an iPhone. As they support AAC over bluetooth, they offer quality audio - bluetooth headphones which don't do indeed sound bad on IOS devices.
