I felt ME got more and more on rails as the series went on. In Mass Effect, there were tons of side-quests you could take on. Mass Effect 2 had fewer but still had very memorable quests, while Mass Effect 3 didn't really have many at all.

Dragon Age has always had exploration and side-quests. Inquisition stumbles due to the lack of focus with non-companion side-quests, but expands on exploration.