This was probably the first space shooter that really appealed to me. It certainly wasn't the first shooter but the game was about as perfect as a game can be in many regards.
Genesis, although revolutionary for its time, had a relatively weak audio processing unit in comparison to the SNES, and in most games this would be very evident. There were exceptions though and I feel as though TF3 was just amazing as far as the music / sound effects were concerned. The voices that you would occasionaly hear didn't sound the best, but this didn't really matter.
The powerups came at you quickly and unlike other shooters i had played, acquiring new ones wouldn't automatically take you away from whatever weapon you happened to be using at the time. You had 5 different attack types and you could cycle through all of them for various situations.
Another great aspect was that if you did die, only the weapon type you were using at the time of destruction was lost.
it was also possible to change the movement speed of your ship while playing. This would become very important during certain stages where you needed to fly in tight quarters where it would be extremely difficult to get through at all on the higher speed settings.
The bosses were huge and varied, and just like any other shooter of this type, understanding their attack methods was critical to defeating them.
One aspect that was pretty revolutionary to me was the fact that the levels were not forced upon you in a linear fashion. could choose which order you wished to approach the first 5 levels. The final 3, which were taking place inside the enemy stonghold, were forced in a certain order.
Later, essentially the same game would be released on the SNES but there were slight variations. While this was not the norm because normally SNES games would be better, the Genesis version of the game was, in my opinion superior. Most of the professional reviewers agreed with this. One of the biggest differences was that in the SNES version, the player was not allowed to choose the order in which they were to compete the first 5 levels and they heads up display was moved from the top to the bottom. I can't imagine why they did either of these things because the original version was fine the way it was.
You can download the ROM of TF3 for free here