ACWW is the original plus some extra stuff topped the wonder of Wi-Fi, all in a DS package that is loads of fun!
Now ACWW surpasses AC by a lot in multiplayer play... well unless you're using the same game cartridge. Unlike the original, all four players in a cartridge are in the same house (I have yet to try out how this works out but it seems like it could get a bit interesting at times!). Then there's the wonder of Wi-Fi. Easy to set up and it's tons of fun to play with other people. To play with others with Wi-Fi, you need their friend code, the only setback but a good security precaution, unless you find a fan site where you can exchange them! One thing to note is that Wi-Fi is far from being flawless. I have more than once met the BSOR (Blue Screen of Resetti where a blue screen with our old friend Mr. Resetti (yes, he is also back in the game it self) comes up telling you the problem and even noting that the game will reset and you'll lose data) so ask the owner of the town you are in to save from time to time.
Animal Crossing: Wild World takes almost everything from the original, stuffs it in a DS, sprinkles on some extra stuff then puts a Wi-Fi cherry to make it a time-wasting experience not to be missed!