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.
More than 1-lane and they're a disaster waiting to happen
So a disaster with significantly better outcomes than a red light runner (with a high speed side swipe or head collision)
From a car perspective, it's just a matter of getting in the right lane for the exit you want.
But otherwise somewhat easier to navigate.
Seems like it's still worse for pedestrians as they have to wait for the beg button.
https://www.mass.gov/doc/massdot-guidelines-for-the-planning...
It provides solid guidance on how roundabouts should approach crossings to minimize risk of accidents or collisions without impeding traffic.
Probably the best graphic is on page 45, figure 5-13
And because they are pedestrian crossings, they only go red when someone is walking across them and for a few seconds before and after. Which means in most cases they are green 90-95% of the time and only go red for less than a minute at a time.
Both as a pedestrian and driver I prefer roundabouts as they force drivers to slow down to non-lethal speeds and there's typically a one car length of road between the turn and pedestrian crossing, so the cars are already going straight when they cross it.
The only road users who don't mix well with roundabouts are cyclists on cycling lanes, as they get in and out of view too fast.
The issue with roundabouts is that drivers never look to the right while entering. We have a few around me in Long Beach and when you're on foot you may as well be invisible.
it's quite useful, if you ask me, it combines the best of both solutions. of course the traffic light has a countdown so if someone presses it immediately after having worked, it will wait for 30sec/1 min before being red again