hmm i believe the second linked one, would only let you output whatever you put into it, at 640x480 interlace 60hz. so if you played a game which wasnt 60hz, then on your screen the game wouldnt run smoothly (you would get jumpy video etc)
the first linked one probably has the same, if not similar problem.
also, with these scan converters, certainly the cheaper ones, they often cant keep up with whats going on, so eg. a fast smooth scrolling arcade game would suffer from stuttering/jumpy video once it goes through the converters (i find those scan converters are better for just watching a dvd movie through it rather than trying to play the wide range of arcade/video games which all have different refresh rates and resolutions).
if the above hasnt already put you off, i also found (with the cheaper scan converters at least) that they added lag, so eg. if im playing a game where i move a spaceship left and right with my joystick, there is lag between when i move my joystick, and seeing the spaceship on the screen move. this seems to annoy some people more than others. personally speaking, i promptly smashed up my cheap scan converter with a hammer.