There'd be quite a bit of friction between the two as it would eventually boil down to control. Neither strike me as the sort of villain who would want to relinquish it.
Kind of like Imperial Japan and Germany during WWII. Sure, they were allies, but the aid they gave each other was minimal and even a hindrance. For example: Japan went to war on the US without notifying Germany of their intentions, accelerating US involvement about a year before they were ready.