It could be that drive, but it could just as likely be other things…a few thoughts:
How much RAM and what drive are you booting from? The problem might be there and not your 4TB drive at all.
Do you have any similar problems when you cut XMBC out of the picture completely and just view your recordings from within EyeTV itself?
Also, just because I'm inherently curious: why are you running such old versions of everything?
Is there any slowdown when you're just using XBMC (or some other player like VLC or Plex) to watch something and NOT involving EyeTV in any way? Close EyeTV just to be sure. Besides checking CPU always remember to check memory usage in Activity monitor whenever EyeTV is involved because historically it has done strange things with it.
100GB free on a 4TB drive doesn't sound like much free space percentage-wise, should it still work fine recording two streams and watching a third, I'd assume yes but I have never filled any of my storage drives up that much. To be safe why not move off about 500GB to another drive and re-test. Is it a 4TB green drive?
You also didn't mention which tuners you're using…is it an HD Homerun?
Do you have another Mac in the house? If so, can you mount that 4TB drive over the network and play back some files? How smoothly and quickly does that go?