Problem with FPE is that you cannot tell if the field has been crypted or not. It is usually used for credit card numbers but the FPE version of s credit card number if it is stolen even though it's not the original number it can still be a valid credit card number and be used by malicious people.
Is FPE as strong as AES the answer is yes and no. FPE on a 3 character string would be a very poor encryption as opposed to if you use it on a 300 character string then it could surpass AES 256. But that would be slower to generate than AES. AES almost have steady speed when encrypting and you can estimate the time it will take depending on the string length and the output will NOT be humanly readable/usuable.
example that are not run trough the encryption for real but just to illustrate the difference follows :
Name : Frank Stall
encrypted using FPE
Name : Steve Moore
Even though the name has been encrypted successfully it is still a valid value usable by people that want to steal identity (remember it's just to illustrate the difference). from the results you can visually tell the value is a name but yourself even if you know it you cannot tell if it's encrypted or not.
encrypted using AES
Name : WOa8+6KskFZ7IdNYgZ3+9BGDJrVfSVd61dDcX1JcVK8=
As you can see if you look at the result of a basic AES encryption the string length don't necessary match, the value is impossible to humanly guess what it is. How can you tell if it's not my birthday i just put there instead of the name.