What Version Which Is In
Both Latias and Latios is available for capture in the game in both Ruby/Sapphire, however, there is a difference on how you can obtain the Pokemon in each version:
Latias: This Pokemon appears in the wild, in the Sapphire version of the game. Also, you can get Latias in Ruby using the Eon Ticket.
Latios: This Pokemon appears in the wild, in the Ruby version of the game. Also, you can get Latios in Sapphire using the Eon Ticket.
Where is Latias/Latios?
After defeating the Elite 4 and watching a TV program about Latias/Latios at your home, either Latias or Latios will be available for capture in the game. As stated already above, in Sapphire it's Latias, in Ruby it's Latios.
Latias or Latios will be out in the wild, in the entire map. There's no telling where it could be, it appears randomly in the entire map. Using the Eon Ticket, you can catch the other Pokemon.
The Eon Ticket is special item you can use in the game. This item can not be obtained in the game itself. You must recieve this ticket from a Nintendo promotion.
Using the Eon Ticket, you can board the S.S. Tidal from Lilycove City to the Souther Island. At the Southern Island, you will meet either Latias or Latios. In Ruby, you'll see Latias. And in Sapphire, you'll see Latios.
Because Latias/Latios appears randomly in the entire map, it's no piece of cake. And even if you happen to run into the Pokemon, capturing it will be one of the hardest challenges you'll face in the game, since it runs away from battle. However, there are things you can do to improve your chances.
Latias/Latios runs away from battle, so you'll have to stop it from running away. To do this, use Wynaut or Wobbuffet, because their ability is Shadow Tag, which doesn't allow the Pokemon run away from battle or be switched in battle. The move Mean Look also does the same, Pokemon such as Golbat and Sableye learns Mean Look.
If you ran into Latias/Latios for the first time, and you didn't catch it, don't worry, you're in luck. After you've seen Latias/Latios in the wild for the first time, it will appear in your Pokedex. This is important because now you can track where it's location is using the Pokedex.
If you have the location on your Pokedex, it's much easier to find now. Using Fly is very critical. Everytime you use Fly, Latias/Latios will be in a different random place. So, if you use Fly and go to a city, and Latias/Latios is near by, then rush over there and start looking searching for it. This might take a couple tries to actually find Latias/Latios near by the city you just flied into. Once you did it though, you might want to save your game, so you can restart your game from your original point if anything goes wrong on finding/catching.
Well good luck! I hope this guide of Latias/Latios has been helpful!