While I don't claim to be able to analyse it frame-by-frame, nor have much experience with the ps2 controller plugged into an actual ps2, my super dual box pro always seemed to get the job done with my dualshock 2. After I lost that, my "usb super converter" that I got seems to work just as well (even though I don't even know who made this thing).
I'm trying to switch to using the arcade stick. Mayflash's stick sucks, but that's why I'm planning on modding it. At least, since it is both usb AND ps2, I don't have to deal with converters when using it on the pc or ps2. With a converter, I used it just fine to play CvS2 on my Dreamcast (though I'm probably worse with a stick at that game than I am at MBAA).