The people in charge of producing the remake were the same people who developed the original game, and they were extremely committed to keeping everything as true to 1990 as possible. The environmental architecture hasn't changed. The enemies are just as aggressive. The items are all in the same place. You can only save on the world map. The most common complaint about the game is that they didn't change enough to update it for modern tastes.

So I would say you have nothing to worry about.