From everything I have seen, the Nvidia looks to be top dog device right now, so that is the most likely to meet your needs (it is also apparently a nice gaming emulation device, but I have no experience with it).
@panteragstk @PENG
I can't remember, is it one of you that runs a Shield???
But, in your case, why not look for a dedicated and locally connected HTPC? Why not just hook up the HTPC as a direct source and get away from remote streaming altogether? Or, at least use HTPC as the streamer?
If you go this route, there are a number of off the shelf options. Personally, I may be looking at a brew your own HTPC solution.