Fatal Fury 3 came out after Samurai Shodown 2 had become a world wide success. While Fatal Fury 3 plays in no way like it's Samurai counterpart, it isn't entirely original, either.
Let me get it out of the way now. Fatal Fury 3 is the best of the Fatal Fury series. The improvements aren't as noticable as from the first to the second, however, I would argue that what they have improved warrants the "sequel".
SNK wisely did not take out anything, and added many new characters to the mix. Something interesting, is the addition of a third level of play. In the previous two, you could fight on two separate levels, usually one that is close to the camera, and one that is away. In Fatal Fury 3 you can fight even closer to the camera. Plus, they have made it much easier to change these levels of play. In this day and age of fully 3D games like Soul Caliber, this fake 3D is pretty laughable, but it's still fun, and interesting to see, nonetheless.
The play hasn't changed much, however, your characters feel a little tighter, which is good. It feels a lot faster, and the attacks are well animated. And both Mai and Blue Mary are to die for. What's not to love.
It's not Street Fighter 2, but it's not trying to be anymore ... now about about World Heroes.