The overwhelming response in this thread should be that Nintendo made the right call when they released a different game than the actual sequel in America and Europe. From a business perspective, Super Mario Bros. was the major sales driver of the NES console, so it had to be followed up by a game that could keep the hype around Mario going. The Lost Levels didn't resonate well in Japan, so instead of making a whole new game, Nintendo reskinned an already existing game and sold it as the SMB sequel. This had the beneficial side effect of Subcon enemies being accepted as Super Mario lore and later on Shyguys became the standard enemy in Yoshi's Island which cemented their place in the larger Mario universe.
From a gamer perspective, Doki Doki Panic is easily the better game. It provides a whole new world on top of having a more reasonable difficulty level. The Lost Levels made hard difficulty a point and introduced two features that no player liked: The poisonous mushroom and warp zones that return the player to an earlier point in the game. SMB laid the groundwork for the sidescrolling 2D platformer genre, but The Lost Levels did hardly anything with it; aside from Mario and Luigi featuring different controls, it was just a harder interpretation of the first game. DDP allowed the player to go backwards in levels and had four different characters along with different mechanics overall. DDP was the proper SMB sequel despite not being a SMB game.