The primary concern with any setup (well, for me anyway), is input lag. That is, the amount of time it takes for what you're doing on your controller to register on the screen. The more processing you add to the signal, the higher the chance of your experience being negatively impacted by input lag.
So, between using a receiver (that will probably process your video signal) and a modern television (which will probably process your video signal again), there is a possibility for some lag.
This is why users might stick to simple amplifier boxes like
this for splitting signals and/or route the signal directly to an old CRT television; you end up with less processing time.
Ultimately, it won't make THAT much of a difference, but I'm pretty picky about that sort of stuff.