There are times that it can take 15 - 20 seconds to open an app after tapping the icon. Furthermore, sometimes when I enter my password to open my phone, it takes a while for my desktop to appear. It seems that this started after the last update. It doesn't happen all of the time, just most of the time.
Slow vs Fast response is really just associated with something putting a load/demand on the processor of the phone. If it seems unresponsive, several things can contrinute to that ... Do you use a LIVE WALLPAPER? Do you have Widgets that are auto-updating too frequently? Do you have Social media sites or email or News or Weather that is constantly updating? All of these can cause slow respone. When did you get the "last update" and was that GingerBread? You might want to try running in SAFE MODE just to rule out any rogue 3rd party apps ... Also, worth Clearing System Cache ... and finally, as others have suggested, a Factory reset after getting GingerBread ..
As Cody said, it could be something running in the background which is slowing down the response time. An apps updating, Email being sent, etc. The same thing happens with computers (which Droid is like a minicomputer). Something running in the background which slows down response time. If it doesn't happen all the time, this would be my guess.
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