I can tell a difference for sure, but I have shot successfully with full-frame, APS-C and 4/3. It's only with the last that I ran into some constraints with throwing backgrounds out of focus, and this was with the 25mm Summilux D. But honestly, as long as my fields of view are covered (in a reasonably fast way), I don't find much difference. I've got a frame, I've got life happening around me, the challenge is to pick some piece of it in time/space and record it.
I'm not a pro, but I've had work from all three formats published. Notably the same subject (restaurants). Though I can see differences, I doubt most other people really can.