Hyper Street Fighter II was included as part of Street Fighter Anniversary Collection, which was released in 2004 in Japan and Europe, whilst the American version was released a year later. In addition to including Hyper Street Fighter II, it also includes Street Fighter III: 3rd Strike.
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.
The main advantage the Xbox version had over the Playstation 2 version was that it had an online mode. Sadly I never got a chance to try Hyper Street Fighter II online -whilst I could get online matches of 3rd Strike all day, nobody ever joined my Hyper Street Fighter II games. The old version of Xbox Live has since been discontinued, meaning the online mode is useless now anyway. It you want to play Hyper Street Fighter II outside of the arcade, this or the PS2 version are your only options, and they're as good as each other.