A question: They're everywhere in Europe, but do they fit the "modern roundabout" definition, or are they more like rotaries or traffic circles?
Some do and some don't, but that applies across the globe. Australia and New Zealand are similar in that they have numerous examples of both types.
To me, to truly qualify as a "modern" roundabout, the approach angles must be right and there must be a shoulder of some sort on the inside to keep trucks from running over high curbs or landscaping. Inside housing subdivisions, these features are usually missing from their "roundabouts" because the primary intent is most likely to slow down traffic. A secondary benefit is beautification. There are less expensive ways to implement traffic control on low volume streets if that was the only purpose.
No matter the type, roundabout signage and pavement markings are frequently used.
Both of the databases mentioned might benefit from having a field that denotes whether or not a roundabout meets whatever definition of modern roundabout is generally agreed upon.
