I have a wired one, and will be upgrading to wireless when I get some spare funds. The wired one isn't too bad, just gets tedious to have to unroll and reroll the cord up, but if you have the money, start out w/ the wireless one.
Started with a wired version, but quickly realized how much better the wireless model is and upgraded. I then bought a used one as a spare but the first one is so reliable (with good batteries) that I hardly use the backup. I have not decided to part with it yet.
Considering the amount of snow on the ground right now in Southern New England, I can't imagine trying to navigate a cord around. Three of the five of us on our winter league skeet team have the wireless unit. One of us has a wireless three-button controller for the system as well, so when we practice as a team, we just hand each other the small remote unit. If you can afford it, which it appears you can, wireless is the way to go. It takes up no space either when you store it, compared to hauling around your own cord.