We went for a trike for a number of reasons.
The compact length, compared to a trailer bike, is a major advantage on winding roads and around the village. It's also much easier to talk to the boys (and with them on front of me, keep an eye on them). I'd be more comfortable with a trailer where visibility was better, where most of the riding was on cycle tracks instead of roads, and where there was more room to manoeuvre. (One of the local mums has a trailgator and it's a real handful to manoeuvre and park.)
Good weather protection was also a must in choosing a bike as we ride in almost all weathers (gales and heavy snow are to be avoided). The boys are well protected from wind, road muck, hail, bugs, rain, snow and anything else. (I get a little grit or ice-blasted at times.

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Safety is very good with the trike, as the crash showed. The front compartment of the Kangaroo Bike has a massive sub-frame plus a roll-over hoop. Despite being hit hard in the side by a Transit, then rolling over, the passenger compartment did not deform. The seats have rigid frames with hammock-type seating and seat belts, while the boys wear helmets while they're inside. I'm quite confident they would have been uninjured had they been in there at the time of the crash.
I'm much less confident about the safety of a bike with child seat. We have one but if the bike drops on its side, for any reason, the child's arms, shoulders, head and neck are very exposed. Should they instinctively put an arm out as the bike falls, a serious injury is likely. We're not put off by this, but riding the bike with child seat means adopting a more cautious and slower approach. On the Kangaroo bike I can be more assertive, ride harder (and faster) and be much less concerned about what the passenger is doing.
Oh, and don't think a trike is inherently more stable than a bike! I've had a couple of near misses due to the handling peculiarities (each style of trike/bike/upright/recumbent has its own handling foibles) and another when the chain came off at speed (ie 25mph or so).