"When it comes to AES vs TKIP for network encryption, there is confusion over which protocol is superior. Each protocol has unique strengths and weaknesses that make them more or less appropriate for certain applications. Despite the fact that AES and TKIP are designed to handle different situations, discoveries about one of these protocols mean it is far less appropriate for use where security is important."
Basically, TKIP is older, less secure and slower. There is no reason to use TKIP over AES unless you have older WiFi devices that are not compatible with AES.
A short comparison of the two:
In essence, TKIP is deprecated and no longer considered secure, much like WEP encryption. For optimal security, choose WPA2, the latest encryption standard, with AES encryption. (If your router doesn't specify TKIP or AES, the WPA2 option will probably just use AES.) However, if you have old Wi-Fi devices that aren't compatible with WPA2, you can use the TKIP+AES or "mixed" mode option if it's available on your router. However, this may slow down your Wi-Fi, since your router will shift into a lower speed compatibility mode (such as Wireless G). So, WPA2 is ideal for security and speed.