As some people have suggested, let's look at SNES/SFC, PC Engine, Genesis/MD and any arcade games that were relevant during that time.
And if for some reason you want to pick something that's debatable for this criteria, by all means just pick it anyway. We're just discussing video games for fun.
16-bit shooters generally aren't as difficult as more modern shmups but gosh darn it if they aren't fun

Mine would be:
1) Winds of Thunder (PC Engine)
2) Thunder Force IV (Genesis)
3) R-Type (PC Engine) To me, the music just really cleaned up the arcade version.