You ask about performance in relation to a Home Theatre PC, but surely the point of a Home Theatre PC is discrete (quiet) media handling.
I wouldn't have thought performance is really isn't going to be an issue (and either should be able to handle it) unless you are going to be using it for other tasks other than just a Home Theatre PC.
Given that a Home Theatre PC is going to be serving up media, films, etc. I would have though its graphics capabilities would have been of greater importance. Unless they have a discrete graphics card (not in your specs) then it depends on what the on board graphics is and that is in the CPU.
I don't know if there is a different (better) Intel graphics in the i5 to the i3, that is something that you would have to check against a more detailed system specification or search Intel for details on the CPU version specification.