I know about the Poison Mushroom and the difficulty of the sequel, but what is the main other difference?
Super Mario Bros.: The Lost Levels was originally called Super Mario Bros. 2 in Japan.
The game was deemed to be 'Too hard' for US audiences, so Nintendo took another game named Doki Doki Panic, reskinned it with some Mario characters, and released it in the US under the name Super Mario Bros. 2.
The Japanese Super Mario Bros. 2 was then released in the US a few years later, but they renamed it to Super Mario Bros.: The Lost Levels to avoid a naming collision with the aforementioned reskin of Doki Doki Panic.
So, Super Mario Bros.: The Lost Levels is the direct sequel to the original Super Mario Bros. game, with different levels and some different mechanics.