Last Ninja 2 was the first one to be released for the Amiga and it was a horribly lousy port.
When Last Ninja 2 Remix was made for the C64 (I guess they made this one since they wanted to put it on cartridge and decided to change the music and add an intro so even some people who already had the tape/disk version would buy it.. I don't know though), they decided to release Last Ninja 1 as Last Ninja Remix for the Amiga. The graphics are pretty nice but the difficulty level is ruined.. the enemies are far too easy to defeat in that version.
Last Ninja 3 is the last one to be released on the Amiga and it's the only one made in-house by System 3. LN3 is my favourite Last Ninja game for the Amiga.