I have both - an iPhone 3GS, and a Blackberry (with a physical keypad) supplied by the office.

Absolutely love the iPhone. It's my third - haven't (yet) upgraded to iPhone 4.

The things the BB does better
- email works much better
- better at picking up a signal, so in dodgy signal areas I sometimes get a signal on the BB but not on the iPhone
- battery lasts longer, although because I'm always doing stuff with the iPhone it naturally runs down more quickly. I charge it every night.

Things the iPhone does better
- the screen
- browsing is incomparably better, in a completely different league
- all the little features like notetaking are much easier
- copy/paste is much better with the touch screen
- it stores texts as "conversations" which is really useful
- the way the contacts book is set up so with a few taps you can call someone, look up where they live (and get the street view of it), send them a text, email them a photo, etc
- all the various apps which make my life easier - BA's, TfL's, Addison Lee's, booking.com's, various newspapers, IMDB.com, etc etc etc
- it's a remote control for my hifi

Overall the BB is better for emailing, but I don't do much of that outside work. The iPhone is incomparably better for browsing and for all the apps. As a phone (ie for making calls on) the BB is probably a bit better.

It all comes down to what you want to use it for. As BOH says, it isn't as good for making phone calls as most non-smartphones or some BBs. But that isn't a problem for me as I typically only use voice calls for 100-200 minutes a month, but usually send 2000+ texts a month (I have a contract with unlimited texts) and download hundred MB of data while browsing.

One major design fault, though, is that you can't use an iPhone if you're wearing gloves. So the easiest way to answer the phone when you're skiing is to tap it or swipe it with your nose. It works with practice but you do get some funny looks.