Just like in the title. I would like to know if I should complete all "ages" for one zone before moving on with the other
Very rarely is it possible to complete each age, in order, for a zone. For example, Bresha Ruins 100 A.F. is near the end of the Historia Crux. Since the very first zone you reach is Bresha Ruins 5 A.F., this is one zone where you won't be able to complete fully until near the end.
Each zone tells a specific story, so it could certainly be useful to do them one after another. However, the ages are scattered across different points in the Historia Crux. Rarely can you continue the same story you just finished a chapter of.
So the answer is, no, you shouldn't complete all ages for a single zone, as that's impossible to do as you work your way through the main story. If a zone is opened up, it's usually a good idea to explore it, at least a little. The game paces itself quite well to ensure you don't get stuck or run into enemies that are too hard for you. Except the Adamantoise. If you run into that without being prepared, your reward is a game over.