I use hotmail as my normal email address and I had to set it up as an exchange email address which is what I assume you had to do. Hotmail offers Push email which is what it sounds like you want. It works the same way Gmail works. When I delete email on my phone it deletes it from hotmail's servers etc and my phone doesn't do the searching for new emails, the hotmail servers push it to my phone.
Does Yahoo offer that or was your Blackberry just actively checking for messages at a much higher frequency than the Shift offers and were the messages on your Blackberry just basically a copy of your Yahoo acount or could you actually delete emails off your phone and have them delete from the servers?
These are the settings I used for hotmail to set it up as an exchange email and even if yahoo doesn't offer push mail you can set the Shift to actively check every 5 minutes, at least I can, though it may drain your battery faster. I believe Push is best for battery life. I realize yahoo may be different but just for example:
Server/URL: m.hotmail.com
Username: Enter full email address, for example:
someone@example.com
Domain: Leave this blank
SSL: Enable this
Then I had to go into the Menu>Accounts & Sync>Exchange ActivSync>Schedule and change the frequency to "Push mail" because it defaults to 15 minutes or some other time under Peak and Offpeak hours. This is where you could check 5 minutes if you don't have a push mail account
Once I did this my hotmail account on my phone works the same as my Gmail account on my phone and I get messages about 10-30 seconds after my real email account gets them. Or you would get them at whatever time interval you pick.
My phone also notifies me of new messages just like Gmail but I had to set that within the email app itself. Once I open the Mail app I go Menu>More>Settings>Notification settings.
Maybe some of what I did to get my hotmail account working will help you out.