Ultimately, the EyeToy was never intended to be used for any purposes besides the ones the software the peripheral was packed in with needed it to do. It followed a very different design philosophy from the Wii Remote (which was designed to be usable in many contexts) or the Balance Board (which was designed to be very functional in a more limited set of contexts). This has a significant impact on how many people will develop for a device, and of course it's software that drives hardware sales.

So which means even technically the balance board was much better than the eyetoy?

Based upon the way the board calibrates, I'm guessing it has four pressure sensors; one on each corner. That way it can determine shifts in weight between front to back and from the left and right sides. The board itself is divided into four visible quadrants

Technically, you can play the balance games with your hands.
I just tried playing "soccer heading" with my hands on advanced and scored 475 pts on my first try. But where's the fun in that?

The other thing about the balance board is that outside of Wii Fit, it's only going to be as useful as any future software makes it.

I think some people may be a little to quick in believing that it will instantly revolutionize console gaming. Wii Fit may well be the best "game" we see that uses it (Skate It could be promising though).

The Wii Remote has because it is the default controller, which was very effectively showcased with Wii Sports.

On a technological level, the Eye Toy is about as sophisticated as the Wii Remote's camera, save that it's a standard camera and not infrared. I don't think it's really fair to gauge either technology as superior, per se, as they follow very different methods and have very different goals in mind. The Balance Board is a real-time tracking device which deals with a constant stream of data, while the EyeToy is a situational tracking device which only reacts when the incoming data changes enough to allow for it. The former has an excessively high level of sensitivity which makes for a lot of error-checking, and the latter has latency issues which make for more frequent tracking errors.

Also the Eye Toy is a rip off of the "Dream Eye".

Dreamcast rules.

The eyetoy was rubbish and did not work very well at all.

The real success was Wii Sports and not the Wii Mote.

Again, software sells hardware. Wii Sports did a great job of this for the Wii Remote, and Wii Fit does a great job of selling the Balance Board (as its ludicrously high adoption rate in Japan and ever-rising adoption rate worldwide demonstrates most clearly). Even with its limitations and shortcomings, with the right software and the right marketing, the EyeToy could have been a significantly more popular device than it was.

The board is extremely precise as a measuring tool, and due to the way the software is designed towards measuring constant, minute shifts in input and translating them into character movements,  I would venture to say that it's a bit more sophisticated than the motion tracking software utilized by the PSEye, which has no way to accurately gauge balance since it uses body reference points (hands, feet, head, anything moving that contrasts with the background the camera sees) for input. 

Or it could just be that there hasn't been any software coded to use the Eye that really showcase its full capabilities. In all likelihood, there never will be either. 

Now if the PSEye had used stereoscopic cameras, that would have been an entirely different issue from a hardware standpoint, but ultimately it still boils down to software implementation.