I use an Elgato HD60 for capturing from consoles that output through HDMI, but it does not work on PS3, because you can't turn off the HDCP encryption on that console. There are devices available that decrypts it for you, but I can't vouch for them as I've never used them. I expect them to introduce some lag, and perhaps degrade the quality a bit.

For PS3 (and PS2, Gamecube and other consoles without HDMI), I use an analogue capture device with component RGB cables (not the standard bundled yellow composite cable). While an analogue interface, this is still good enough for 720p/1080i, and the very minor analogue signal interference you might experience will surely be minuscule compared to the quality loss you get from the compression done by your computer prior to streaming it. For this, I use a Roxio game capture pro, but I can't recommend it to others as I find the software bundled with it terrible, and it doesn't play nice with OBS and other streaming programs.