Actually I'm probably a little more productive... with the way I use a smartphone. Voice controls on my DROID are much better, and the Car Mode that reads and replies to text and emails really helps me out. ... voice assistant on BlackBerry was nothing in comparison.
Emails... I do miss the gestures, but I can create and reply to emails, I can add attachments of all kinds (even without a built in file manager), with the BlackBerry keyboard I've got flick to type... what's not productive?
I use my camera a lot to take pictures of customers sites... camera software for organizing images is much better. And the fact that I can just shake my phone to start taking pictures is also much more productive... for me.
While I miss the red blinking light, full notifications on the lock screen work just fine for me.
Web searches... again Google Now has increased my productivity there by a lot.
I think it comes down to what you are use to and comfortable with.