Batrider is quite nice because it gives you busloads of shmup fun but does not tend to overwhelm the player with esoteric gameplay elements like Ikaruga. It's not my fave shmup, but it's always good for a game or two, and it's shortness comes in handy for score hunts.
Basically, it's kinda dumb to compare Ikaruga and Batrider, but that's another can of worms. I play Batrider for different reasons than Ikaruga, and I bet that goes for most shmup'ers out there.
About Battle Garegga, well, I love it. It doesn't have all the bells'n'whistles of other games, but it's great fun, and challenging. Try to 1cc it and you'll see what I mean.... some games do not "open up" before you really get down and play it for score, that's the difference between the older and current shmups. IMO, Garegga is better than the sequel Battle Bakraid, but that's prolly just me I guess.... man, I love shmups with planes, tanks and military stuff, Garegga, 19xx, the Strikers games, etc. Oh yeah, and that's right, "R-Type Final it ain't", because it's a vert shmup, not a horizontal one...
Another Raizing title I like is Soukyuu Gurentai. The ST-V original looks way better than the SAT and PSX ports, but it's kinda fun to play.