Let the hive mind of Engadget get that for you.
"We need a digital camera that can be switched on and fire off that first shot fast. It's not a commonly tracked statistic on any review site, and nobody seems to have this information for every camera. We were hoping other readers could inform us as to what small digital cameras can fire off their first pics in under a second (ideally under half a second). It needs to be small, but mostly, just really quick in operation. Thanks!"
Since they have redone the entire user interface in Flash on the Premier, the processor speeds aren't really comparable. It may well be that the new UI is actually SLOWER than the UI on the existing Tivo Series 3 or HD boxes. We'll have to see. The existing demos don't look too impressive, regardless of the MIPS improvement of the CPU.