Signals these days are remarkably clever.*The traffic signals in any large town or city will be controlled by a SCOOT controller. These signals all talk to each other to ensure all the signals operate efficiently together to allow the primary routes in the city to flow as well as possible. (I.e. green followed by green followed by green then one red, repeat as you head out of town). The whole route of a town will be managed. You obviously can't dynamically manage roundabouts or priority junctions.*
Traffic signals allow pedestrians to cross better than roundabouts, and are more likely to be considered if there is an accident trend at this junction involving peds. This is of rising importance as ped subways slip out of favour.*
Traffic signals are considered when there is a relevant vehicle accident trend (side swipes, false starts being rear ended) as they are generally safer on th basis that they remove the decision whether to go or not.*
They can gave slightly higher capacity during peak hours because of this removal of 'thinking time'.*
Roundabouts are not effective if vehicle flows on each arm are nor equal-ish. You may well find the predominant turning movement at a roundabout blocking off other arms. Signals allow smaller arms to a chance to flow as required (see detector loop below).*
Modern signls use detection loops to detect if there is a vehicle queuing at the signal head and also at the back of the queue. During peak hours, if the signal detects a vehicle on this rear detector it thinks 'right I'm running out of queue space, it's my turn to be green next'. This either completely informs or overrides the signal timings (i.e. its pattern or sequence). During non peak hours it will have different timings as the predominant turning manoeuvres will change and the rear detector will not come into play. During the night it may operate on an all red basis- when a vehicle arrive at the first detection loop of any arm it will put that arm straight to green and then back to red when the vehicle has gone.*
Traffic signals need much less land than a comparitive roundabout. This is usually the first and final issue when considering a comparitive roundabout
Traffic lights are cyclist friendly and in some cases incorporate advance cycle stop lines. Traditional British Roundabouts are not.
Yes they're not perfect- some signals will not have great off peak timings or too long 'intergreen' timings but when used appropriately and designed well (and with modern signal equipment) they do theirjob well. The chances are that in many cities, the large junctions are all going to be over capacity and nothing you can do in the available land will have enough capacity. The signals just manage the available capacity as well as possible.
Hopefully this has been at least slightly interesting!