The Playstation 2 version was released in Japan in 2003, with versions available in America and Europe a year later. In Japan, a special edition pack version was released which included a combo DVD, a mouse mat and some other extras. America got the best deal though, as Hyper Street Fighter II came as part of Street Fighter Anniversary Collection -which also included Street Fighter III 3rd Strike. In Europe, Hyper Street Fighter II was released as a stand-alone game.
This port features everything from the arcade version, along with some other extras. A training mode has been added, allowing you to practice moves and combos, and has several different settings. Street Fighter II: Movie is also included, all though it has been edited to remove the swearing and some of the violence. There is also an option to use the CPS1, CPS2 or remixed versions of the music (the remixed versions are taken from the 3DO port of Super Turbo). New versions of Cammy, Dee Jay, Fei Long and T. Hawk's themes and ending themes have been created for the CPS1 versions of the music.
It you want to play Hyper Street Fighter II outside of the arcade, this or the Xbox version are your only options, and they're as good as each other.