WPA traditionally uses TKIP cipher while WPA2 uses AES cipher.
WPA2 has 2 main advantages
- Stronger security (although honestly WPA is actually still pretty good for home use)
- Allows proper adoption to 802.11n with regards to negotiating above 54Mbps
WPA has an advantage over WPA2
- Better compatibility across the board (older and newer devices can both take advantage of WPA)
If your router supports WPA-Auto just make things simple and just use that. If your device supports WPA2 it will automagically use WPA2 as the preference.