Email is pushed to your BB automatically.
Email push on an iPhone is quite effective (even with an older iPhone with the old iPhone OS 2.x), although turning email polling on and enabling 3G at the same time eats battery life like there's no tomorrow. (Literally... as in there won't be a tomorrow for your iPhone unless you recharge it tonight.)
My iPhone ties into my work email via Microsoft Exchange ActiveSync. When I click "Send" in Outlook, my iPhone will typically chime to indicate a new email message has been received in about 5 seconds. Far faster, I'll note, than how long it will take the same copy of Microsoft Outlook I just used to send the email will notice that there's a new message in my inbox. (I always CC myself for improved email searchability reasons....)