Blackberry's have "Push email".
This means that a copy of your email is sent to your phone as well as sitting on your POP3/IMAP server waiting to be downloaded onto your PC.
You can read the text of the emails, but HTML looks terrible.
You can view attachments such as images & pdfs.
You can reply and delete (either from the phone or from the server).
NB When you delete emails from the server they are still there in the Trash folder. Some companies include Trash towards the server limit and don;t empty it automatically after x number of days, so you may need to log on to webmail and empty your trash or face losing emails because senders get a "Server full" message.
WiFi enabled Blackberries means that you can use an existing internet connection rather than using your mobile connection's data service.
On my "Orange" Blackberry Pearl I have found it nearly impossible to connect to public WiFi hotspots in airports, but can connect to my home network.
Once connected to my home WiFi, I cannot see any significant speed improvement over the "Orange" connection so I turned it off to help battery life.
My Orange contract includes unlimited data so this is not a problem.
Surfing is OK, especially if you have very few expectations on speed and as long as you can get a good GPRS signal.
Download Opera Mini as a separate browser for the Blackberry - much better than the Blackberry default.
The Blackberry camera is rubbish and you can't get many decent games for it! May not be a big concern for you though.
Beyond that I know very little about the iPhone other than it seems rather pricey and looks rather swish!
It can probably do a lot more than the Blackberry but I don't know whether it does email better - I have heard some people complain about the touch screen keyboard.
My wife loves her Blackberry Curve for emailing (full qwerty keyboard), and I get on fine with the 1/2 qwerty on the Pearl.