It's more like the later. Mostly linear with some side quests here and there
I disagree, the world map is 100% old school FF after Act 1. I spent hours exploring all the areas I had access to before continuing the story. I went into a place called the Dark Shores even though it said "Danger" and nabbed some nice loot off the floor while dodging aggro including a Lvl 23 Picto with 1000+ defense on it. ALso also found two Gestral Beaches with mini-games. I found and beat up some of those Chromatic NMs too.