The real Internet is on the iPhone. Flash is not available yet for the iPhone, but my Pearl doesn't play Flash files either. YouTube is available on the iPhone, but Flash embedded in websites will not work. Media capabilities may very well be much improved on the BB, but still absolutely pale compared to the iPhone.
The mail app on the iPhone is far and away a better experience than the BB. I'm not talking about push or BIS or security or any of that stuff. I get push mail and the "enhanced security" is lost on me. I am talking about once the message is open on your device being able to view it as sent. The iPhone will also open doc, docx, xls, xlsx and pdf files (all the formats that I use) directly for viewing. No large 3rd party app needed. Audio files sent as attachments (like from my voicemail provider and voice memos in MP3, WAV and M4A format) play seamlessly with a click. The BB sort of does as well, but there are extra clicks and another application slowly loads the message to listen to.
The iPhone does not multi task, but you still get notifications when you have a new email or SMS message. There are IM apps that also provide push notification of new messages. You can also listen to music and run other apps like Mail or Safari. That's all of the multi tasking that I do. That said, when I click a link in a message and go to Safari I can select Mail and be right back in the message where I left off.
That's not multi tasking at all, but that's close enough for me. Given that my Pearl has a great deal of difficulty managing it's meager allotment of memory I'm not sure if multi tasking is a feature or a curse, but the BB does multi task.
The on screen keyboard is different at first but I am now quite used to it and have no issues at all typing out even longer messages. I wouldn't say that I prefer one keyboard over the other, but after a few days the on screen deal become very easy for me. And no, WiFi does not automatically get shut off after a set amount of time. I wasn't aware that it ever did.
As mentioned, there is an overwhelming number of apps available for the iPhone. A great number are just fluff but there are some really fun and useful apps to be had and the ones that aren't free generally don't cost much. Google Earth, Kindle, TweetDeck iTunes Remote, DirecTV and Paper Toss are my current freebies and I love them all.
Neither the iPhone nor the Blackberry are a one size fits all solution. Go to a store that has working (Internet too) demo phones and try both. Go back multiple times if you need to, but make up your own mind by holding each in your hand and trying them on for size.