Well... speaking as a breeder/exhibitor of boxers, and an owner of a bulldog - with a close friend who breeds and shows. I can tell you that BOTH breeds are equally suited to children.
I can tell you the boxer has a higher activity level, and is a more boisterous puppy. An adult Boxer is more of a visual deterrent to possible 'baddies' but personally, I dont rely on my dogs to protect my home. LOL
I enjoy both boxers and bulldogs - but the MOST IMPORTANT part of the decision between the two is CHOOSING A REPUTABLE BREEDER.
In these two breeds in particular, moreso bulldogs - the health and longevity GREATLY varies from a bad breeder to a good one. Our bulldog has NO skin, or breathing issues. Hes a VERY healthy, low maintenence dog.
But temperament and quality really has moreso to do with who is breeding and raising the litter - the BREEDER is who plans the breedings, and makes the decisions.
With either breed, considering the size - I would tell you to just be DARN sure you choose an ethical breeder.