No idea about the DP1, rogue_designer, but in my experience I'd say the GR-D is less than 100ms. I'm not a big action shooter, but non-anorak friends who've borrowed it say it's much better than their digicams and they say they can capture what they see. I can feel the lag, but then I'm used to the near-instant response from an RF or good SLR... or I'm just highly sensitive...
The GR-D's definitely worth a try ot see whether it bothers you, and it seems to be used successfully by people who do go for the decisive moment stuff.
It's also metal, and you can put external viewfinders and funky Voigtlander gizmos on it, just like a proper camera! 😉