Within this genre (and this is true of most other currently popular genres as well), the camera is the most important thing defining what happens in your game.
A freely scrolling camera is good for selling a wide sense of space, and making everything feel continuous. Challenges involve enemies attacking from off-screen, and players missing features of the world which you'd intended for them to discover, just because the player happened to wander a little too far to one side or the other.
Fixed cameras are good for ensuring a consistent play experience. When correctly corralled, you can ensure that every player will see the same screens, and the same features of the world. Which means that players won't miss things the same way that they can in freely scrolling worlds. Fixed cameras are good for delivering bite-sized individual challenges (as in individual rooms in Zelda), where monsters from one room can't interfere with the desired challenge of other rooms. Fixed cameras are also conducive to having a chunky "grid" layout, which makes it really easy to show players a map of what they have and haven't explored yet, which can be a lot harder to communicate when you have a freely scrolling camera. Cons of fixed cameras is that you have to constrain enemies within the view of the fixed cameras (players will consider it unfair to be attacked by enemies they can't see), and that you really need to standardise on a single aspect ratio for your game, so you can be sure that everyone sees the same things from each camera, no matter whether their screens are 4:3 or 16:9. (ie: letterboxing or pillarboxing will be required, in full-screen modes)
If your game is about exploration and/or collecting things, you probably want a fixed camera. If you want the game to be about solving puzzles, you probably want a fixed camera. If your game is about quick reflex challenges, you probably want a fixed camera. If your game is more procedural (enemies are smarter and can chase the player over long distances), then a scrolling camera is what you want. If you don't want to carefully design individual encounters, a scrolling camera is what you want.
Either sort of camera will work. But depending on which sort of camera you make, different types of game mechanics will be more or less effective. So decide what you want the player to do in your game, and then pick the style of camera that's most appropriate for the game you're making.