What do you get if you do?

Basically... what happens upon completion of the Sinnoh Dex? For example... in Emerald the proffessor would give you a choice of the jhoto starters.

You get the National Dex. After you complete that, you have beaten the game, basically.

no you dont cause u get the national dex after the league

no, national dex you get after you complete the sinnoh dex, which you would have to get by beating the league, as some pokemon you wouldn't be able to find easily otherwise are found in the elite four's pokemon rosters.

After completing the sinnoh dex, you will obtain access to pal park, and you will obtain the pokeradar.

Hmm maybe I haven't phrased this well. I meant after you've CAUGHT all the Sinnoh Pokemon.

No special reward for catching all of the Sinnoh Pokemon I don't think, you'd don't get anything after the National Dex as a reward.

catching all of the pokemon in the sinnoh dex nets you nothing. Sorry

Not even a star on the trainer card? I'm pretty sure it earns you one of those.

nope, sorry, not even that. Here are the steps for getting the stars(no order required)

1.Enter the Hall of Fame after beating the Elite 4
2.Complete the National Pokedex (EXCLUDING EVENT PKMN)
3.Win 100 consecutive battles at the Battle Tower
4.Get Master Rank in all contests
5.Get the Platinum Flag in the Underground (by stealing others flags, sorry not sure how many)

and when it says complete national pokedex, i dont know if it means catch all pokemon, or see all pokemon.

Catch. I used AR. Don't use it. though. You don't get all the Pokemon. I did it on Pearl, it doesn't give you all the Pokemon. It just says that you did, even though you didn't.