Giratina has by far the best design. I like Rayquaza, but to be honest it looks like a glorified snake. With claws. And Kyurem.....can't say I'm much of a fan. As for stories, Giratina's rules. It is the master of the distortion world, the rumored third to Dialga and Palkia's legend duo, and a boss Platinum role. Kyurems is cool too, the remnants of Zekrom and Reshiram. Rayquaza controls the skies which is ok....but not real winner material. As for who wins in a fight...I have to give it to Rayquaza. Kyurem is weak as HECK, and although Giratina could crush Kyurem and has excellent stats, Rayquaza's attacks and speed are too high. But, yeah!
But my opinion could be a bit off. Giratina was my favorite Pokémon ever since I saw it on the commercial for Platinum, and is the entire reason why I gave Pokémon a chance. Before that, I loathed it. Giratina's game, Platinum, was my first.