In addition to the below, this anime has been released on VHS, but the video versions are obsolete these days.
Viz released Fatal Fury Double Impact in 2000, which is a single disc release featuring both Legend of the Hungry Wolf and the second special on it. It has both the English dub and the Japanese dub with English subtitles. As with their Legend of the Hungry Wolf VHS release, this version features a slightly edited intro -the text scroll of the title now displays the English title of "FATAL FURY" rather than the Japanese "GAROU DENSETSU", and the logo reveal also now has the English title. "Fly Away", the song which plays during the end credits, was not dubbed and instead has English subtitles. The credits were also translated into English, although only the voice actors and actresses for the English dub are featured on it.
The "to be continued" frame is different, featuring the English logo on a black background and an altered font for the continued text. Extra features include chapter selection and some concept art. The concept art accidentally spells Hopper's name as "Hoper".
Discotek released Fatal Fury: Legends of the Hungry Wolf on DVD in 2014. Like Viz's DVD release, it features both Legend of the Hungry Wolf and the second special on one disc. Also like Viz's release, it has both the English dub and the Japanese dub with English subtitles. The box mimics a Neo Geo game box. The extras are a "credits" option, which plays the English credits sequence from the Viz version of New Battle -their credits for the first anime aren't present. It also includes a gallery, which contains a few pieces of promotional art. This version also features the Japanese opening title and credits sequence. This means the text scroll of the title displays "GAROU DENSETSU", and the logo reveal also now has the Japanese title.
The Japanese credits are also slightly different to Viz's version, as they don't start as early -there aren't any credits when Terry is on the ship, they start after that scene. The original "to be continued" frame is also present, which features the Japanese logo on a blue background.
Whilst it's stated to be a region 1 DVD on the packaging, this isn't the case and will play on any region of DVD player, unlike the Viz version which is region locked to region 1 only. Sadly neither of the specials were remastered, which is what I wanted the most. So really if you've already got the Viz Double Impact DVD, there's not much point getting this one as well. However...
In 2021, Discotek surprised everyone by announcing a new Blu-ray set, which would include the two specials, and for the first time, both would be remastered! I don't currently own this version, but from what I've seen of it, this is definitly the best version you can buy. It includes subtitles for when the song "Bye Bye My Love" is played (previous releases have not had this), and also includes a special feature a lot of fans have been after: a kind of vocal-only version of "Bye Bye My Love". What this special feature does is play the song with the dialogue removed, but sound effects, such as crowd noise, can still be heard. It's still the closest anyone's gotten to releasing a vocal-only version of the song though.