Here's the full story from Wikipedia (the last sentence turned out to be wrong, though):
As the AES version of the game was approaching its release date on July 8th 2004, it was mysteriously delayed a week, moving its release date to the 15th. When it came out, the whole Neo Geo community was shocked to see that not only were generic fatalities removed, but the zetsumei ougi was watered down to a loosely based version of the issen for the characters. As a first, this act of censorship affected the entire worldwide release, not just the non Japanese speaking audience. Not only did these modifications censor the game, but the censorship also created bugs, such as that of the AES's exclusive training mode.
Upon hearing fan outcry, SNK did a cart recall shortly after that which fixed the bugs brought about by the censoring acts, and also to restore the character specific zetsumei ougis, but only partially. The acts of body splitting were still long gone, which made some of the zetsumei ougis make no sense. However, some of the more violent content still remained, such as the more violent death screams and being able to be smashed into a wall. 
The only way for players outside of an arcade to experience the zetsumei ougis was either through emulation or to get an unfixed version of the game and apply Razoola's Universe Bios to it, which allows access to the uncensored versions of the moves and fixes the bugs that the modifications did. Despite this, the version included in Samurai Shodown Anthology will retain the gore of the uncensored arcade version in the English version (The Japanese version didn't include SSV Special due to development time.)