Rotary just means traffic circle, nothing more. Thus a rotary could be a roundabout, but doesn't have to be. A roundabout is a specific type of traffic circle that follows certain important design standards, the most important ones resulting in limited speed. Narrower circulating lanes, smaller diameter, and sharper entrance angles all reduce speed, thus improving intersection efficiency and safety.
Also, in general a circle is much safer. You have in effect removed the possibility of the high speed broadside collision, which are the most dangerous at traffic signals. When people crash at a roundabout, its either arear-end (same as a signal, but less often) or a narrow angle, sideswipe-type collision. They may result in damaged fenders and egos, but probably won't kill you.
Also, I agree with the above post about aesthetics. A roundabout is much more attractive than a traffic light, and generally actually requires less pavement in the end, since you don't need all kinds of turning lanes. Note that I mean less pavement, not less land, since the circle does usually occupy more land.
