Really fast. Not really any delay except for whatever it takes for the antimation to bring up the call screen. I'd guess less than quarter of a second.
If you have TVOut2 Mirror TVOut app installed. Make sure its not enabled.
It took me a day or so to figure that one out after I jailbroke and restored. for some reason it enabled the TVout and I didn't even notice it even though it was right there on my SBSettings. My phone was acting REALLY sluggish sometimes, even just closing an app folder and sliding to another screen would sometimes freeze for a couple seconds. But once I just disabled TVOut (You only need to enable it, if you are actually outputing to a TV) it was a fast as can be.