A lot depends on your lifestyle. Bulldogs tend to be pretty easy keepers. Just make sure you get one from a reputable breeder who shows his dogs to their championships and screens for genetic disorders. Stay away from newspaper ads, pet shops, and people who just breed their own pets to make money. Whatever breed you decide upon, go to the national breed club's website. They usually have breeders listed by geographic area. This is the best way to find a breeder who is bound by the club's code of ethics, as opposed to someone who's just out to make a quick buck.
Both breeds that you are looking into would be a good choice, but I admit that my knowledge of the Besenji breed is very limited. I am an proud American Boxer owner, but I would not compare them to English Bull. I have a couple of friends that have one or two, and they all LOVE theirs. I will tell you that if you get an English Bull, you will have to wash and clean those deep folds of skin, they have a tendency to become infected. They also are very strong, almost from the word go. Given their unusual strength, and combine that with their mass and low center of gravity, and them add on top all the muscle that they have, if they decide to go in a direction that you don't want them to go (until they get trained) they will give your arms and legs a serious work out. They have a great amount of personality and become very attached to all members of the family. They snore........
I would like to congratulate you on getting a new member to your family.............