Yes it certainly depends on where you are. If I'm out in the desert or above treeline (like in the High Sierra), I prefer off-trail. In heavily wooded areas, certainly sticking to the trail is preferable to bushwhacking, etc.

It definitely feels like more of an "adventure" when you are off-trail, but whether it turns outo be a grand adventure or an unpleasant one is the question.

Another consideration is that if you become sick or injured, it is better to be on a trail, where someone will probably eventually find you than out in the middle of nowhere where they won't.