For both the AppleTV and FireTV, is the Youtube app just a thin wrapper around youtube.com/tv? There doesn't seem to be that many "native" Youtube apps around - it kinda suffers from the same problem that Netflix does in that someone's decided to code for the lowest-common-denominator device [1]. I've heard the Netflix experience on AppleTV is pretty good.
1: WTF, Netflix, why would you remove proper Kinect support from the Xbox One app?