There are quite a few differences once you go more than skin deep. Obviously, one uses copper wires while the other uses electromagnetic waves, but the protocols, speeds, and transmission control procedures are all different. Wired speeds are mostly 10,11,100,1000, and 10000 Mbs where as wireless has many more speeds, from 1 Mbs to 600 Mbs. So, you can see that wired connections are faster based on pure speed. What also makes wired faster is the transmition control and how the speed is divvied up. In a wireless network, the max speed is the maximum transfer rate for all devices conbined. So, if 2 devices are on a 54 Mbs wireless network, the total bandwith for both is 54 Mbs, not 108 Mbs. On any modern wired network the reverse is true, each link is seperate.
In a wireless network, the transmission media is shared, so there is a protocol that prevents two devices from shouting at the same time, resulting in a garbled mess. On modern wired networks, not only can all devices transmit at the same time, but they can transmit and receive at the same time.
Security is a biggie. It is very hard to impossible to eavesdrop on a wire inside of a building you have no access to. Wireless on the other hand leaks everywhere and can be hacked by anyone with a little computer skills and the right training.
Despite all the disadvantages listed above, wireless is the most common choice for connections in the home. With laptops becoming more and more popular and wireless technology getting cheaper the hassle of running wires starts to become a huge minus. Besides, most homes never need the speed a hardwired connection can offer.