Similar, but much, much worse. That was a Steven Spielberg-produced anthology show that got a guaranteed 2-season commitment from NBC due to Spielberg's name, and it was pretty much a showcase for directors. And like many director-driven projects, it was heavy on the style and spectacle but weak in the concepts and writing. A lot of its stories were very superficial, simplistic, entry-level fantasy stuff, or were just really bad. It looked really good, but it was often painful to sit through. The Twilight Zone, by contrast, has always been more of a writer-driven show, especially in its original and '80s iterations. So it was much stronger in terms of concepts, plot, dialogue, and characterization.
Also, Amazing Stories took its title from a classic science fiction magazine, even though it had no direct connection to the magazine and simply licensed the name.