I'm pretty sure that the Saturn port of Strikers 1945 does allow scores to be saved, as does the Saturn port of the first Gunbird. I haven't played Strikers 1945 II in some time, but I think that one does let you save scores as well.
Psikyo did 4 2-game packs on the PS2. 2 of them are generally considered fairly poor, rushed ports, while the other 2 are quite good.
Strikers 1945 pack and Gunbird pack are usually considered problematic. Gunbird has issues in the port from what I have read, and both strikers games have reported issues. I've never tested the games myself, just because I have heard this information from several sources.
Sengoku Ace Episode's 1&2 will give you access to Sengoku Ace (Never ported elsewhere), Which I believe is Psikyo's first shmup after leaving Video System. Sengoku Blaede is on this pack, and is a good port, but you do lose the option to play as Marion, which is available in the Saturn port. So, I would recommend the ps2 port here, just because an additional game beats an additional character in my books.
Dragon Blaze/Sol Divide: Probably Psikyo's best and worst games in this pack. Not to talk smack on Sol Divide, its really unique.... REALLY unique. Focuses on melee, plays very different from the usual Psikyo stuff. Dragon Blaze alone is worth this pack though!
If you ever have a random question about a shmup just ask away, could talk about them all day

Edit: Nice Avatar!
Oh, do you happen to have an xbox 360? The shmups on that system will blow your brain... over and over and over and over