There are two downsides. They really require much more space than a traditional intersection. They also remove "traffic gaps" between major streets that permit people to make a left hand turn out of a neighborhood.
He's not a huge fan of 2-lane roundabouts. They create an incentive for drivers to cheat by driving down middle of both lanes, staying at 35/40 rather than slowing down to 25 go around the round about. They also cause confusion when someone gets into the wrong lane (left/center lane must go straight through) and this reduces throughput. Perhaps there is a minimum/maximal traffic where they work effectively.
After using roundabouts at nearby intersections, I'd also add that they are much more attractive. Waiting at a light causes stress (and people tend to "text", causing more delays). Given the chance, I prefer to take routes that use roundabouts. I've timed them, and they are faster and more consistent then traditional 4-way-lights, especially at intersections where left/right hand turns normally cause traffic backups.
[1] http://www.annarbor.com/news/roundabout-planned-for-geddes-a...