As I recall virtually ALL the guns we have seen with cracked frames have been box locks. there is a lot of steel hogged out in the action body of a boxlock.
In the grand scheme of things, we haven't actually seen very many broken guns. The Coggy "Avant Tout" models are gaining a bit of a reputation for failing recent English reproof, but, other than that disquieting fact, a broken gun is rare. I think recent English reproof is pretty high, higher than those guns were ever intended to see. A few Yank models will develop cracks, if abused.
There were likely 10-20 boxlocks built for every sidelock. I'm guessing the bit about sidelocks getting more frequent, and better maintenance might have something to do with longevity, as well.
I'm a lot more concerned with how well I shoot any given design, than any asthetic considerations. They can all be pretty if they are finished up nicely, and, I shoot them well.
It really doesn't matter how beautiful a London sidelock is if I can't shoot the thing worth a damn.
Best,
Ted