...as does the BlackBerry - built in.
Its down to essential needs, and personal preference.
For me, having flawless email, social networking and IM capabilities is far better than having an App Store.
For others, having games and apps that make farting noises is better.
Alright.. I'll play the which is better game.
The Blackberry devices were built more or less with email in mind so it doesn't surprise me that they are better for email. How much better? Well that is debatable.
I use my iPhone to check 6 email addresses which get around 100 - 200 emails per day between them. The iPhone works very well for this and gets push email from Yahoo and MobileMe within seconds every time. It is cheap and effective for what I need to do.
IM is handled purely via third party applications so it depends which choice you go with. Beejive is my choice and it works great. I get push alerts when the application is closed and it works very smoothly for everything from basic messages to file transfers. I even get Jabber support with enough options to log into our Jabber server that barely any desktop IM client can support because of the strict configuration. IM+ is also looking promising, but I haven't tested it as much.
Social networking isn't something I deal with much since I just find the whole thing pointless. My friends use Facebook, Twitter, Loopt and many others constantly on their iPhones without missing a beat so I assume it works well. They're always excited over the new Facebook application so I take it the software works well enough.
I can use VNC, SSH, Email, IM (with excellent Jabber support), Air Sharing via Wifi (look up the application for what it does), Last.fm/Pandora, and many other applications just day to day. The iPhone isn't perfect, but it is better than any Blackberry I've ever used in so very many ways.
Oh and the real kicker is the comparison between the browsers. The browsers available for the Blackberry aren't bad, but Mobile Safari is the gold standard at the moment. I can use it with all our complex AJAX helpdesk software without a single error. That means a lot for getting my work done.