In my opinion the impact of the camera startup and shot to shot times has been overstated. In practice it doesn't feel that slow to me, and I have no problem pulling out the phone, unlocking it, starting up Pro Cam, and taking a picture in a short amount of time when I'm in a hurry. Yeah, it could be faster, but it's never been a problem for me so far. And you can switch to the stock camera app if you want things to be faster. You still get the oversampled 5MP image in that case which is good enough for almost all uses.
Web browsing is decently fast (a big step up from my WP7 phone, a Samsung Focus S) but not as fast as a PC or Nexus 4. I still try to avoid following a link and then hitting back, opting to instead open it in a new tab and then close the tab, because I know it's going to take a while to re-load the page I was on. Honestly I think IE is the problem here, not the 1020. IE !@#$ing sucks.
Email is super fast, but it was on WP7 as well. This is just something that WP does well regardless of the hardware. Of course it's not a very demanding task.
App performance is good but could be better. The same apps run noticeably faster on the Nexus 4 - for example Skype, Words by Post, Ruzzle. But it's not as big of a difference as exists in web browsing.
As for updates, aside from a few settings moving around, the phone is as it was at launch.