I'm running version 5 of the OS. And the problems with the web browser are mostly just it's not that good of a browser although it has improved. But once RIM releases a webkit version of the browser (hopefully next year) it will improve significantly. That said though, I don't browse much on my phone anyway, as I use RSS feeds or apps for most of my data, and whip out the laptop and tether for real browsing.
Battery power is good on the Storm, I'm not sure how much it has improved on the Storm2. I can kill the battery in 12 hours if I do a lot of bluetooth tethering, but if I'm just using the BB for regular use and phone calls, you could probably last that 18 hours (more likely with the Storm2). But is it still no multi-day phone by any means. I have to charge the Storm nightly. But... unlike the iPhone, you could get a spare battery if you wanted to.
Call quality I have never had an issue with. Seems to be quite good, and that's from experience being on both ends of the call (my wife has the Storm too, as we got the BOGO deal).