I think I recall actually using an actual Amiga one time (seeing as I have the emulator, and trying to find good games to play on it). Looking back, one of my brother's friends possibly owned one and had a handful of games. A couple that come to mind, and considering how long ago it was, I doubt he remembers them either, that I can't seem to recall the name of them are like this.
1- You played as an eight-ball rolling upwards (usually) probably trying to make it through a labrynth. Usually had green, grey, white, and black as the main board color scheme (maybe had other colors, maybe green was for easier levels). Some levels had chess like rules to navigate (otherwise you go bye-bye), others were a race to the finish, and others were like the game Labrynth, where you had to avoid a bunch of pits and navigate a maze. The viewscreen in the game was probably a 7x7 grid, and if you moved fast enough, the 8-ball was closer to the far end to make you more aware of what's up ahead so you can time your jumps better.
2- Maybe it was The Incredible Hulk or something, but I remember a game that had a more Contra-like feel to it (mostly scrolling platformer). You played as a trooper/commando or some green dude or something, and the first level (I think) you're fighting your way through the jungle. I think it begins beating up your targets with your fists, and then eventually getting better weapons or something. I think you could enter doorways as well. Surprisingly involved for an action/adventure/arcadeish game.
It's been easily 15 years ago since I last played them, but those are the most details I can extract from my memory archives. I know it had to be on an Amiga, because I don't recall any other machine (other than the old Dos systems) that could compete with those graphics, 8-ball game aside.
Any luck on my first request about some kind of tank game for the Commodore 64? I remember it had Tron's level of control where you can control the turret and movement separately as well. May have been the age, maybe I was too young to play effectively, may have been because I was still rather new to advanced games back then, but it was pretty hard, but had surprisingly good graphics for the time (maybe made in the same time frame as Raid Over Moscow, the graphics were that good, if memory serves correctly).