Other than Mighty Final Fight, there was no Final Fight game released for the original Nintendo Entertainment System, at least officially. Fans have created a version of Final Fight 3 for the NES, unofficially, why the series was not started with the first is unknown but this game is interesting nonetheless.
Firstly, this is a port of the SNES version, almost every level and every enemy is included- all four playable characters are available. Some slight changes were made, think of this in comparison of the SNES Final Fight 1 versus the arcade version- some liberties were taken. For instance, weaker enemies are recurring, not just on specific levels, but all of them. There is also no longer multiple paths in the game, players are now restricted to a single path, similar to the first Final Fight.
There are cutscenes but they contain a lot of typos and errors. The screen is shrunk by a black bar at the bottom that features the game logo and current round information. Fans of Mighty Final Fight will notice the re-use of music and sound effects in Final Fight 3.
There is a TON of flicker and other sprite errors to be seen in Final Fight 3 on the NES. That is understandable, there is a lot of things going on on-screen, too much for the NES to handle.
The only places to grab Final Fight 3 on the NES from are sites that host other non freeware files so we cannot link to them directly.