No there isn't any performance differance, but if your web server doesn't know what to do with a file type .inc then it just passes it as text to the browser opening up a security hole.
Try it, call your .inc from your browser and see all the code and information that you are trying to protect get easily displayed to you users.
If you use .php and your server knows what to do with .php then it'll parse it and nothing that isn't supposed to be displayed will be displayed.