For me, it varies. I do use the backwards compatibility on my PS2 and Wii for PS1 and GameCube, respectively. As long as it emulates by hardware/firmware (like those do) and not software to hardware (like the 360 with XBOX discs), I'm down with it. I make an exception for the Wii Virtual Console, XBOX Marketplace, and 3DS downloads, though, as they seem to be done properly.
When I can, though, I do prefer to use separate systems. I figure the less wear and tear I put on an older and potentially harder to replace piece of hardware, the better off I am long-term.