The wireless Mighty Mouse uses laser tracking, while the wired uses optical. To put it simply, laser tracking is far more accurate, which is important if you are doing photo work, gaming, etc. The WMM is also bluetooth, which means you don't use up any USB ports, which if you have a large number of USB devices is good.
I like the Mighty Mouse (I have the wired version), but when I was looking at prices, I found the price of the wireless MM to be too much so I got a RF based Microsoft Wireless Mouse. Problem is it uses one of my two USB ports, so I might consider the MM or another bluetooth solution in the future. Its a matter of price, and choice. If you want the 360º scrolling that only the MM can offer, then go for it. If you want to save a few $$$ look at other brands. Logitech , Microsoft and others offer some great mice. Laser mice are more expensive and the MM is about right in terms of what it offers though.
The advantage of wireless is easy to see, no wires all over your desktop, and freedom of movement, no strings attached, bumping your hand... having to push the cord out of the way etc. The disadvantage, as with any wireless mouse, it needs batteries, and batteries die. That said, my mouse is almost four months and and still has the originals, not bad if you ask me. Now, MM have the known issue of clogging scroll wheels, that you have to keep in mind. There are ways of dealing with this issue, and I find the 360º scrolling in photo files to be worth that small bit of effort to deal with it.