For example, in California, people in the roundabout have right of way. But sometimes there are confusing traffic lights in the roundabout:
https://www.google.com/maps/@37.3911304,-122.0805522,3a,75y,...
In New Jersey, on the other hand, sometimes, the subjectively most "major" road has the right of way both going in and out of the roundabout. People already in the roundabout have to actually stop for the major road people to enter the roundabout. If you're on the major road you can theoretically pass through the roundabout and not worry about the fact that it's a roundabout. A couple examples of this is seen here, where you're IN the circle but have to yield to incoming traffic:
https://www.google.com/maps/@40.5027947,-74.8525293,3a,75y,2...
https://www.google.com/maps/@40.5761533,-74.6286047,3a,75y,2...
Although the UK seems to be going towards more lights and fewer larger roundabouts.
https://www.google.com/maps/@42.4011187,-71.1170306,19.36z
Try as we might to keep chaos at bay with our laws, stop signs, and blinking orange lights, it peeks through the seams when you watch the traffic patterns there.
In fact France has several dozen different signs that as a US driver I had to learn and relearn. My wife who grew up there keeps pointing out my mistakes every time we visit.
There's no way that's true, is it? What circumstances would a four way stop sign allow for more traffic flow than a roundabout?
I'm pretty sure it's purely cost-cutting. Four way stop signs are extremely cheap compared to roundabouts. There's no other advantage that I can think of.
Roundabouts are safer (there is no opportunity for t-boning at a roundabout), faster and simpler to navigate than four way stop signs (a roundabout you just give way to people already on the roundabout, a four way stop sign requires you to keep track of who arrived first and then do a weird dance if you both arrived at the same time, and you still need to watch out for people attempting to go out of turn -- which is not possible with a roundabout)
As for t-boning, you can definitely have someone enter a roundabout early/late and hit another car on the side, or dart in front of a car that's in the roundabout (especially possible if the roundabout is not perfectly circular) and themselves get hit on the side.
And people manage to go "out of turn" in roundabouts all the time, by not yielding, or by tailgating.
Heavy traffic. In most situations a roundabout will do better, but when completely saturated, the 4-way has a slight advantage. This is probably due to how 4-way stops with dense traffic develop an predictable alternation pattern that eliminates ambiguity and reduces the clearance requirements.