Works through airplay as well if you have a receiver capable of that, not sure what kind of quality to expect. I mean, you could always go through ebay and a third party vendor for those adapters and pay much much less, but quality is always a worry. I bought a third party minidisplay port to HDMI adapter for like $5 and it works fine as far as I can tell, which isn't to say I disagree at all. The price makes it almost useless unless you have airplay or already have the adapter.
Either way it runs through the receiver so I wouldn't expect the differences to be that great whether going through a blu-ray player or from the phone.