OMG shmups are the best.
I been addicted since 1980. Williams Stargate, a.k.a. Defender II was and in many ways still is my all time favorite. I used to leave blood on the control panel back in the day. Stargate was the first coin-op in the collection and remains today.
If you have a Saturn and can find a copy, Radiant Silvergun is phenomenal.
Similarly, for PC Engine, Rtype, Blazing Lazers, Gate/Lords of Thunder, and if you have the arcade card, get a copy of Sapphire. It's the equivalent of Radiant on the Saturn. I almost went to Italy to buy an original copy of Sapphire for $700 over 10 years ago. You can get very nice bootleg clone copies of Sapphire for $60 bucks now. Some people try to pawn clones as originals, so it's not worth seeking an original if you are into that sort of thing. I have a lot of Japanese imports and had I known about the future collectability of some of these titles I would have kept all the spine cards. I could kick myself for that now, but those games aren't going anywhere.
If you like Musha on the Genesis, try Spriggan on PC Engine. My favorite shooter on Genesis was probably Gaires or Thunderforce3.
It's not shmup, but a beautiful game, but if you like platform games on the PC Engine, you must play Dracula X. Why NEC did not bring that to the USA just makes no sense. PC engine was my favorite system overall.
So many good PC engine shmups never made it to the USA, same for Saturn, and all the other consoles.