Circuit training is weight work plus cardio, done in circuits: a few minutes of cardio, then maybe lower body weights, then upper body weights, then back to cardio, etc. Full body workouts are weights only. The weight work in circuits is usually a bit lighter than in weights-only workouts.
I guess the benefits would depend on what you're looking for in a program. For example, if you want heavy weight work to gain mass, full body workouts would be better than circuits. If you really like variety and moving around, circuits would be fun. There are a lot of different factors.
I personally despise circuits, so my opinion is NO, you do not have to use both in a rotation. I just got rid of all of mine! :7