Quoted By:
Nah. Luxury ball is the best. After you catch a mon, it will double any happiness points they receive in friendship-raising activities. When you trade it and the pokemon's happiness resets, they'll still have luxury ball's effect to help boost their happiness quicker. Dusk and Quick ball's effect are only good WHEN you're catching a pokemon. They don't offer any benefits AFTER you caught it.
The only other ball that has long term benefits is the Friend ball. If you catch a pokemon with it, it will start will 200 base happiness. This won't matter when you trade it and its happiness gets reset. BUT, any pokemon bred in a Friend ball will start off with more base happiness than non-Friend ball offspring.