I use a mini-pc (a little asus eeepc box with a "who cares" intel cpu in it and a nvidia gt620m running openelec). The reason is actually simple: A lot of the embedded processors are much more finicky in terms of hardware decode.
I used to run geexbox on a TI OMAP4460, and it worked wonderfully, right until you hit a track with DTS or DTS-MA audio, and then because it was not hardware supported, it fell right down and couldn't even play at 3fps. Maybe with XBMC now having a new audio engine (This was in the XBMC 11 days) the world is different.
The hardware decoders were also not quite as resilient to restart and had occasionally random failures compared to the nvidia chipset , which were very annoying when watching movies. I have never had this happen on anything in the nvidia/amd/intel world, and anything that can't be hardware decoded, the intel can absolutely handle.
Given the very low idle state of the newer haswell chips, unless you had a strong desire to not be intel based, i'd see if i could find a mobile motherboard and run openelec on a 15w TDP mobile haswell (or at worst, an itx motherboard and core i3 haswell).
Basically, these boxes are fun if you want to futz, but just aren't really "living room ready" unless you have a very fixed set of source video/audio.