Without looking up statistics (and I'd love to be proven wrong here), I'd be willing to guess that roundabouts may result in some marginal increase in minor accidents but massively reduces fatalities or accidents that leave the pedestrian in the ICU.
Additionally with a roundabout the crossing can be moved a few cars down the street away from the roundabout itself so that cars can have line of sight to safely approach the crossing and pedestrians have time to react to incoming vehicles. On top of that proper placement of crossings allows a normal zebra crossing to be upgraded to a pelican, puffin, or toucan crossing without impeding flow of traffic within the roundabout.