Japanese DVD
This DVD was released in 2003. Just thought I'd put it up here because it has a couple of things I want to mention. Firstly, the cover art, which was also used on the video release and some other promotional material, features Robert wearing game accurate clothing, but he is never seen wearing that brown jacket in the actual anime itself. Secondly, during the credits, Yuri Sakazaki's voice actress is listed as Kaori Horie instead of Ayumi Hamasaki. Kaori Horie was Yuri's voice actress in the video games during the time this was released, but she never voiced the character in the anime. Why this change was made is unclear.
U.S. Manga Corps DVD
Originally, U.S. Manga Corps released Art of Fighting on video in 1997. But a more up to date option would be this DVD, which was released in 2003, and is region free. Featuring an English dub or the original Japanese audio with English subtitles, this is the best version to own, if you have to own it. Extras include a fight montage video, an art gallery, chapter selection and some previews of other anime releases.
The dub has Ryo at one point state Yuri is 19, even though the bio King brings up for her later states she's 17. This was presumably changed due to American age of consent laws.
This version features a new credits sequence. The usual credits used in the Japanese version are still there, but after those finish, another set of credits appear for the English dub. U.S. Manga Corps also made a couple of errors on the packaging, claiming that the man who directed this -Hiroshi Fukutomi -also directed Fatal Fury 2: The New Battle. He didn't direct that one, he directed the first Fatal Fury anime. The back of the box also misspells Ryo as "Ryu".
Finally, the game history in the extras claims Art of Fighting 2 was released in 1993, but it was actually 1994.
Image Entertainment DVD
This DVD was released in 1998, and it was allegedly also released on video. The DVD has the original Japanese dub, and the English dub (featuring the same dub as the Manga Corps DVD) is also present.
It also has chapter selection, but I believe that's it in terms of extras. The original Japanese credits sequence appears to have been cut from this version, and only features the English dub credits, the same ones as seen in the Manga Corps DVD.