That's really interesting that the problem doesn't occur in other browsers, only in Chrome. That suggests that Chrome is doing something different with its full screen video presentation than the other browsers.

I know that once upon a time it was possible to set YouTube to have different playback methods (for example HTML5 versus Flash), but I no longer see that option. However it might be interesting to check: Maybe Firefox+IE are using a totally different player method.

Another thing to check is the quality level of the data stream. When you get bad frame rates, what is the video quality of the playing video set to? If it's the highest setting, does the frame rate get better if you take it down a notch? And if you get good frame rate on the other browsers, are they defaulting to a lower quality setting than Chrome?