The former is not common and they're called traffic circles. They're pretty much obsolete nowadays, true roundabouts are superior. The only reason to even include traffic circles is in case someone wanted to recreate a famous one like the arc de triomphe.
However, traffic-lighted roundabouts are common enough in Britain at least and cars do have to stop on them.
I don't know if I've understood correctly... Do you say that roundabouts like Arc de Triomphe are obsolete? I'm sorry but I no agree at all.
Where I live are very, very common and useful for traffic congestion. Actually City Halls build many roundabouts in new districts
and old intersections that need it.
But you'll be able to build roundabouts or not in your city
PS: Big roundabouts have traffic lights but not inside.