It's pretty much as simple as the title. What is the best for the situation at hand, primarily FSC, but other situations as well? And what is the best overall choice for general use/ FSC use?
Grey Owlite Sheild vs. Volcanic Plate Sheild vs. Crest of Almire
There's certainly no answer in general. An elemental shield such as Grey Owlite is popular due to gun puppy projectiles and Vanaduke mask projectiles. Barbarous Thorn Shield is popular because of the sword damage bonus. Swiftstrike Buckler is popular, especially among gunners, due to the attack speed increase. Crest of Almire is popular because it's a shadow shield, which is good for fiends, and its statuses are useful. Volcanic Plate Shield is popular because trojans and Vanaduke's mace do a lot of normal damage.
In FSC, it really depends on your level of expertise (and that of your team), and which parts you find difficult, and how much you lag. Many people use GOS because they already have it and its defense is good. Once they get CoA, they might use that instead, because of all the zombies in FSC. But once they master FSC, so that everything but Vanaduke is really easy, then they might switch to VPS, or switch back to GOS, to have the best shield for the Vanaduke fight. Some sworders use BTS, and some gunners use SSB, because they don't need serious defense.
VPS is a good overall shield, nice resistance, the best for Vana mace and good fire resist.
CoA A shield for Slags Walkers and Slag Guards, nice fire resist too.
GOS Good for Phase 2 and 4.
I'm not sure why, but I've been seeing Grey losing popularity in FSC. I think VPS is best if you solo, CoA if you're in a somewhat reliable team.