You just post this just now. Of course no one will answer you this quickly. I am glad that you decided to get rid of your Sidekick 3. It's garbage!
As for web browsing, you will notice some differences but not much. Keep in mind that the web pages go to the Danger server first to compress it and arrange it so it will show up somewhat nice on the Sidekick 3 browser.
No matter if you get the Blackjack or Blackberry 8100, the pages will show up very similar.
I put together a chart comparing different smartphones from T-mobile. It's available here. http://www.geocities.com/sk3vsbb8100/
The only phone that comes close to the Blackjack from T-mobile is Dash.
Keep this in mind, if you going to Cingular from T-mobile, you will pay more. T-mobile have the cheapest prices around.
And if you thinking of tethering (using your phone as a modem for your laptop), you will pay $74.99 (when you sign up with a new contract) for data plus your voice plan on Cingular.
If not, you will pay $29.99 for Cingular vs $19.99 for T-mobile for data plus voice plan.
T-mobile's data plan already allows you to tether too.
As for streaming video, no, the Blackberry 8100 does not do that so you may want to go for Microsoft based phone if you want that.