Most notably, you can't plug a second controller in, meaning also that the Famicom microphone (which is embeded in the player 2 controller) cannot be used. Also, the system can't hook up to the Famicom Disk System. The Familator also suffers compatibility issues with a few games, including Bases Loaded.
GAME Watch did a side-by-side comparison of the Familator's TV output of Xevious to the Wii's Virtual Console version of the same game, and found that the colors and the sound were inferior, even without taking into account the Wii's ability to use component and D-terminal connections. Battery life was, of course, also an issue.
None of these concerns are exactly dealbreakers, but even as a novelty it would be hard to justify the expense of such an item without excellent performance.