Yes, Rayquaza and Giratina appear in their respective versions’s stories.

Platinum’s storyline is more similar to DP’s than Emerald’s is to RS’s.

With Platinum, the biggest change is to the climax, which adds a short quest through the Distortion World before battling the Team Galactic Boss and getting a chance to catch Giratina. Aside from that, the changes mostly boil down to a few additional scenes here and there, which are all quite brief but do serve to flesh out the characters a little more. Though there is also a significant change to the progression, as instead of bypassing the Hearthome Gym when you first visit the city and forcing you to backtrack after earning your third and fourth Badges (as in DP), Platinum has you take on the Hearthome Gym when you arrive there the first time (the Gym Leader’s levels are adjusted accordingly).

Emerald has more substantial divergences from RS, but only to an extent. The overall progression is mostly the same, but the story now has both Team Aqua and Team Magma play antagonistic roles, instead of focusing on only one or the other. To make room for this, there are a couple of additional confrontations with Team Magma — once at their new Hideout (a dungeon exclusive to Emerald) near Mt. Chimney, and once at the Mossdeep Space Center. At the climax of the story, you also have to travel to the top of the Sky Pillar to awaken Rayquaza, whereas the Cave of Origin (where you battled Groudon or Kyogre in RS) section of the story has been truncated, and Groudon/Kyogre are left to be battled and caught in the post-game.

I wouldn’t say that either game ends “earlier” — the climax occurs at about the same time as the original pair of games, just with the new cover Pokémon added into the mix.