When it comes to improvements to their predecessors, Emerald because of Battle Frontier and it had all the gen 3 Pokemon obtainable without trading.
Otherwise, Platinum because it's the most recent gen.
That, my friend, is untrue. It was missing things from both Ruby AND Sapphire, so you were required to trade with both to get all the Gen 3 Pokemon. I did it in order to get the Johto starters in my Emerald.
Yellow was a nice improvement on Red and Blue, but the anime tie-in game makes it feel weird to me. I do, however, enjoy that you can get all three starters.
Crystal honestly didn't make a huge improvement on Gold and Silver. It added the first Battle Tower, animated sprites in the beginning of battle, and kind of featured a Legendary Pokemon in the story. It was an improvement, but not a major one.
Emerald made the storyline many times better and added one of my favorite functions in Pokemon ever (the Battle Frontier), but lacked the significant Pokedex improvements I felt Hoenn needed. Though I think a remake of Emerald would take the cake as greatest Pokemon to date.
Platinum made a big difference to me. It addressed some glaring flaws from Diamond and Pearl. It updated the regional Dex (HUGE problem from DP), updated sprites (aesthetics, but whatever), added the Battle Frontier (though it isn't as nice as the one from Emerald), and made the storyline much better. That means that Platinum wins for me, but only by a small amount. My only complaint is on the stupid looking jacket your character is forced to wear. :/
White FC: 4727 7422 4019 Platinum FC: 2063 5286 9480