The german magazine "Amiga Games" published a complete 6 part development diary ( The long way from Turrican 2 to Turrican 3 ) in 1992.
The history of Turrican 3 / Mega Turrican is quite long and interesting.
Factor 5 began the work on Turrican 3 for the Amiga right after Turrican II was released in 1991. They had a working demo that already had some features from the final game. However, around this time, the Amiga market was already in decline and together with Rainbow Arts, it was decided to develop the game for the Sega Mega Drive. The game was completely redesigned for the console and it was co-developed by Factor 5 and members of Kaiko. Kaiko then approached Rainbow Arts and asked to develop their own version of Turrican 3 for the Amiga. However, development on this version did not get very far and was stopped after a short time.
Development on the Amiga version was restarted, this time as a conversion of the Mega Drive game. The programming was done by Peter Thierolf, formerly of Kaiko (the company was falling apart at the time).
Turrican 3 for the Amiga was finally released in 1993, and even though the Mega Drive version was finished earlier, it was released as Mega Turrican only in 1994.
The main differences between the versions are graphics (the 64 colours of the Mega Drive version had to be downconverted to 32 for the Amiga) and sound (the Amiga had the more advanced sound hardware and thus the music tracks sound more impressive on it). The main gameplay difference is that a secret level in Mega Turrican became a regular level in Turrican 3.
Sources: Power Play magazine 10/93, Messages from Julian Eggebrecht, Peter Thierolf and Frank Matzke at http://www.nemmelheim.de/turrican/bonusfiles.php