When your computer is in one room and the rest of your audio system is in another you usually have more than one way you can connect the two--via wired Ethernet or wireless WiFi. Sometimes physical restrictions such as distance, layout, or the physical makeup of your home will be decisive in determining which method is most practical. In terms of fidelity each method has its appeal. Hard-wired connections offer more robust data throughput and are less likely to suffer from dropouts and data loss. Wireless connections allow your computer to be completely isolated from the rest of your system, which can eliminate any noise problems caused by AC, RF, and EMI.
Once again, since each connection method has its own particular advantages and disadvantages it's impossible to make a blanket recommendation about which is sonically superior. I've used both wireless and hardwired connections with my computer audio systems and found that wireless connections are definitely more prone to dropouts, but the complete isolation between the computer and the rest of my system is comforting. The best solution is to try both connection schemes and then choose the one that combines more ergonomic and sonic advantages.
Just like the arguments about whether nature or nurture is most important to human development, the discussion of whether software or hardware is more critical to sound quality in a computer-based audio system will probably continue well into the foreseeable future. Obviously not only does your choice of playback software have a major impact on the sound quality of your computer-based audio system, but how that software interfaces with your hardware will also affect your hardware choices. Just because one user finds a particular piece of software produces optimal sonics doesn't mean that you will have the same results in your system. Sometimes software decisions won't be clear-cut. When forced to weigh ergonomic ease against ultimate sound quality, different users will make different choices based on their own priorities. While iTunes is convenient, it doesn't offer (and doesn't claim to offer) the best playback quality; however, improving upon it does require additional effort in setup and day-to-day operation.
Probably the most often asked question I've heard during 30-plus years in audio is the query, "Which is the best?" I despise this question because it means that someone wants a simple solution to a complicated situation. The art and science of high-end audio has always been about exploration and discovery. Computer-based audio is no simpler than high-end audio. Fortunately, the more you explore and the deeper you dig, the more sonically rewarding computer-based audio becomes. We are only at the very beginning of what will be known as the "computer-audio age." It will be a wild but entertaining ride.