I went with the PDP TE MK9 for one reason: I burned out my thumbs playing MKD incessantly and obsessively. I can't play more than half an hour without fatigue and then pain. Worst of all, the longer I play, the worse I got because the fatigue lead to input malfunction. I can't comment on the learning curve since I switched back and forth between the two, getting frustrated with one then the other. Finally, I've settled on the stick. No choice really, unless I want to play for 20 minutes at a time, a few times a day.
With the stick I can play for hours and hours, and not only do I not get fatigue or pain, but I get more accurate. At this point I wouldn't go back to the pad even if I could. While some things are a bit easier on the pad, others are much easier on the stick. Everything is a trade off. However, as I grow more comfortable with the stick I'm noticing that not only is there anything I can't do with it, but I'm doing them consistently. In other words, the longer I play, the better I get.
As for the game being built with one or the other in mind, I lean towards the stick.
To simplify: Try it long enough to learn it, and then you'll know if it suits you. For all you know you may discover that you're better and happier playing on it than the pad. Only one way to find out.
Last, I would suggest you try (if you can) the "X" configuration of the PDP and the Madcatz/Qanba (the latter is for PS3/360/PC) layout of four over four. What I find is that the spacing between the buttons is a bit far in the "X" formation, and squared up---as opposed to the ergonomic slant to accommodate the natural curve of the hand (Madcatz/Qanba).
*You mentioned Kabal's instant air blasts, and I can say that there are best to do with a Hit Box. I can do them consistently on the stick, but not fast enough so that they hit a standing unblocked opponent. They go over the head by a hair. Maybe it's me. I may not be good enough to do them fast enough yet. But I believe they can be done, just easier on a HB. Dash cancels are easy enough, along with everything else.*
**It's much easier to use Reptile on the stick since the back-forward motion is so much faster using your wrist on the stick than thumb on a pad. Again, might just be me, but I would never choose the pad over the stick for back-forward motions, or half circle rolls for Tsung's soul steal and Kano's ball.**