I know I'm late to the party, but I saw this and wanted to correct it- Rayquaza has Dragon Ascent. Plus, if Rayquaza could get an Outrage off, which it most likely could with it's high speed stat, Giratina would be as good as gone. You could also give Ray something like Weakness Policy to buff it even more, or something else to make sure it doesn't die straight-away. Overall, yes, I'd say Giratina has the better design, much as I hate to admit it(Go Rayquaza!), but Rayquaza would have a much better chance of defeating Giratina in a straight-up battle. Also, given Rayquaza's speed and power, it's better for going against most pokemon anyway. It's been on my Emerald team for a while, and absolutely destroys the Elite Four- Even the ice type leader, as I just give Ray a quick claw or weakness policy. This is just my opinion, don't think I'm discredition yours- I just wanted to point out that Ray learns Dragon Ascent, and it's turned into a rant- Sorry about that!As much as I agree that Emerald is the best Pokémon game to date, I have to go with Giratina. I like the Sinnoh Dragon Trio a whole lot on the fact they're largely unique Pokémon with astounding designs that control forces beyond anyone's comprehension. They also have a very intriguing relationship and backstory, which is the best made for every Legendary group as of yet in my opinion.
Though Dialga is my favorite of the three, Giratina comes very close. It's got an awesome and different design, has two Formes that change drastically in design and appearance, has an unique Type combination (One of the coolest and most unexpected, as well), and has a more interesting relationship with the other two. I loved all of its involvement in Platinum, too.
I like Rayquaza, don't get me wrong, but it's got a more generic design (Even if still awesome), a Type combination we've seen too much already, and is also one of two Ubers without a signature Move (Eruption and Water Spout aren't exactly signature for Groudon and Kyogre, but it always felt as if it belonged to them more than the other Pokémon that learn it, much like Meteor Mash for Metagross), which lets it down. It does have a much cooler Ability than Giratina's two Formes, but it still falls short.
Not sure who'd win a battle, but I think Rayquaza might be the most likely victor. Still, I gotta go with Giratina, as it's way more unique and interesting.