Wireless has great convenience over wired technology - flexibility, portability and no tangling or ugly cables. But there was traditionally one caveat with this - wireless stuff didn't sound good. Period.
However, long gone are the days when wireless headphones were significantly lower in the performance stakes than their wired compatriots. technological experience and development have helped, but perhaps the most significant leap in performance quality for bluetooth wireless audio was the emergence of the aptX codec chip into mainstream products.
What is aptX?
Bluetooth audio information uses compression, which is the curse word of audiophile standard digital audio. Compression can cause data loss in transmission meaning less detail and poorer sound quality than other formats such as CD or vinyl, for example. However, there are different types and levels of compression. . .aptX put simply, uses fewer bits per digital sample which means smaller files. The key is that to get the best sound quality both devices ave to be aptX capable (ie. bluetooth headphones and a smartphone - indeed, most current smartphone models are). Then you will get an impressive near-CD sound quality without wires!
Does wireless really sound better?
As a rule, any half-decent pair of wireless aptX headphones will sound better than your bog-standard buds supplied with your phone, end of argument. If, however, your standards are ultimate audiophile clarity and staging, then perhaps you need to stick with wired over-ear or in-ear multiple driver options. A nice compromise can be found in products such as the 1MORE MK802 which has excellent quality sound and the option of both wired and aptX play!
Ultimately, the solution is that which best meets your needs. For moist people wireless designs will sound as good as wired in most cases. With great recordings and a good source a high end wired design may take the honours, though. In the gym or on the move wireless aptX will give you flexibility and freedom to move around and be active whilst listening. On the other hand if you want to sit and concentrate on your music and only the music then your optimum choice is to go for a wired high-end design that will also use audiophile-standard copper cable where the priority is ultimate sound quality above all else.