Only difference is the redesigned Turbo function (which I never use anyway) and the lack of a Home Button on the PS2 models.
I have an HRAP 2 SA (blue button model) and a standard HRAP 3 modded with Sanwa buttons. Quality’s the same.
I really don’t detect a difference in response, either. I’ve used both sticks (HRAP 2 SA with a PS2-to-PS3 adaptor I bought off of e-Bay) and they play the same on SF IV.
Main thing I like better about the HRAP 3 is the Octagonal Gate I installed. (The Home Button is a bonus, too, but I could just use a stock PS3 control pad for that as well. Not a big issue for me.) The Octagonal Gate generally makes pulling off the Ultimate and Super Combo moves easier. I have found, however, that after about a week you hardly notice the stock Square Gates installed in my other sticks. You can differently get better with the Square Gate if you have an Octagonal Gate installed in another stick – ie, experience with a better controller/more comfortable controller makes you better with less comfortable/inferior controllers.
Same thing happened with me playing SF II on the SNES. After I got the Capcom Soldier Pad, my SF II playing improved dramatically. I found I could go back to the godawful stock SNES pads and pull off special moves that I could never get to come back. Still preferred the more comfortable D-pad and traditional 6-button layout on the Soldier Pad, however…