A boxed stroller properly packaged and checked into the hold as checked baggage may be less likely to be damaged than even a gate-checked stroller, but then you'd be without a stroller where you need it to make it to the gate for the flights. Also, boxed strollers/checked-in luggage seem to be more likely to miss the flights than gate-checked strollers.

Do note that even when airlines/airports accept strollers to be gate-checked for gate-delivery, it doesn't necessarily mean the transited/destination airport will gate-deliver the stroller. Some airlines at some airports have ground handling agents who won't gate-deliver gate-checked strollers even when the strollers are tagged as valet/gate-check-for-gate-delivery baggage. In such circumstances too, a wearable body-carrying baby/toddler carrier can "save the day" when a passenger's airside stroller plans don't work out for whatever reason.