What I think is the major problem with Brawl's online is that Brawl looks too good, and the game play requires very fine accuracy. There is a compromise between accuracy and fast-processing time.
Mario Kart Wii has its drawbacks: first, the graphics mirror that of the GameCube, so the art design, whether it be in local play or online play, is uniform, unlike The Conduit, which apparently had its graphics toned down and made ugly compared to the rest of the game for online. Second, when playing online there is a lag between player and item collision, but given Mario Kart's luck-based game play, it's doable and appropriate. Because more processing power was given to handling 12 players from anywhere in the world rather than excellent graphics and direct hits, it is a very smooth online, with no bad lag or slowdown.
Brawl on the other hand, was made to take full advantage of the Wii's hardware for local multiplayer, more or less. Thus backgrounds are busy and bursting with activity. Even the stages with no obstacles have a lot going on. And Brawl requires accuracy. Without it, punches would fly straight through characters. Thus, Brawl has a laggy online since only is it processing actions from up to 4 consoles around the world, the events that follow, and the surplus of detailed, busy graphics. If the developer was be able to give Brawl an online that does not compromise graphics and accuracy for fast processing time but still have smooth online no matter what, it would be a miracle.