Danes and Mastiffs are very similar in size and temperament...and they're all 'leaners'. The tails do help their balance, so not usually bobbed. One of my pups got so excited once that she whipped her tail and knocked over a 7' tall, wrought iron plant stand, including plants.
Both Danes and Mastiffs are able to acclimate to most living conditions, including apartments, but they do need some outdoor exercise. Mine were very easy to housebreak because they are very intelligent. I was very, very lucky. My first Dane was pick-of-the-litter from two champions, AKC registered, and the lady let me take him home for $50. He was a treasure.
I had one Dane (my favorite) who lived to 12. He grew up with a litter of kittens, so none of them were really sure whether they were cats or dogs. Imagine a 90 pound, 6 mo old puppy, all long legs, big feet and huge ears, trying to climb a tree with the kittens.
One word of caution, if you get a dog of that size, take him to obedience training (the sort where you train the dog). They really don't realize their own size and strength, and need to know the rules. I took all three of mine and it was lots of fun.
Mastiffs are brachiocephalic, and sometimes have respiratory problems related to that characteristic. Also, like the SharPei, they have to have the folds on their faces carefully cleaned, and often, to prevent skin conditions.
Is your neighbor's dog English, Neapolitan, Tibetan, or some other distinction of Mastiff?