I play x-box 360 on a 56" Samsung DLP RPTV. From these forums, I learned that the input lag on my tv using component cables was terrible. But if you used the VGA adapter, the tv did significantly less processing and the input lag was minimized. I tried both, and found a significant improvement using the VGA input. I never researched the input lag over HDMI (and never tried it on my tv) because the 360 didn't have HDMI when I bought mine.
Is there any reason to believe that any of these projectors would have less input lag over VGA than another input? Also, if you are outputting a 1080p signal from your PS3 or 360, might you have less lag since the projector would not have to do any scaling?