It has been said, that the Ultimate Shoot Em Up systems are Saturn & PCE. They’re not.
The System with most shmups is the AMIGA.
It has more shmups than Genesis, SNES & PCE put together:

AMIGA
http://www.classicgaming.com/shmups/xenocidefiles/amiga.html

SNES
http://www.classicgaming.com/shmups/xenocidefiles/snes.html

Genesis
http://www.classicgaming.com/shmups/xenocidefiles/megadrive.html

PCE
http://www.classicgaming.com/shmups/xenocidefiles/pcengine.html

PCE CD
http://www.classicgaming.com/shmups/xenocidefiles/pcenginecd.html

SEGA MEGA CD
http://www.classicgaming.com/shmups/xenocidefiles/megacd.html

And one more interesting factor that has been over looked by many is the fact that the PSX has as many if not more Shmups than the Saturn:

PSX
http://www.classicgaming.com/shmups/xenocidefiles/ps1.html

Saturn
http://www.classicgaming.com/shmups/xenocidefiles/saturn.html