So what are the advantages and disadvantages of these two controller styles as far as shmups go? Is it just a matter of personal preference? Does using one or the other affect your technique? Not that I've had much joystick experience, but it would seem to me that a joystick would be clumsier to use than a normal controller, seeing as you'd have to move your whole hand to the side (a lot of work for your wrists) just to do what I could do with the flick of my thumb. I doubt this is a big factor though, as I've seen some amazing shmup and fighting game videos from players using sticks.
A lot of people complain about getting blisters from normal controllers, but I've developed quite the callus on my left thumb, so that's not a big deal for me. Also, it seems like if you want a stick that it's best to go for a high-quality one, which can set you back quite a bit of cash.

To give some perspective on where I'm coming from, my favorite pad of all time would have to be the stock SNES controller. Best d-pad ever, in my opinion. A close second would be the fabled Saturn pad, which I've become acquainted with recently. The PS2s isn't great but it get's the job done alright. I love the DC as a console, but it's controller is a complete piece!