A purist would say that neither sentence is correct. The verb should be singular "wants" because there is a choice of one other. If you said, "Neither dogs nor wolves are willing to attack a porcupine." The verb becomes plural. Admittedly, this rule is broken so often that most people wouldn't pay any attention. Similarly, the rule of who versus whom is broken so often that you can hear well educated people breaking these rules and no one is shocked.

“Neither” takes “nor”. “Either” takes “or”.