Bloodborne's story is arguably as good as Dark Soul's. Many people find that the tale of hunters gaining power through the ages by defeating the demons of the cosmos an interesting story. Like Dark Souls Bloodborne has tons of lore, every item and weapon ties in with both the world and the characters in it. There are reasons for there being every beast where they are, and reasons npc's act how they do.
Dark Souls has way more bosses that makes the game so much more interesting. Including the DLC the bosses and items in there make sense for being there like the old iron king dlc ties in with the main story by giving details with the Fume Knight being allies with Velstadt by being "brothers" and being loyal to the king. But Bloodborne doesn't tie in with the game with like dark souls does with all the details and dark souls has 3 dlc's while bloodborne has 1 dlc that basically has it's own story inside of it.
Though Dark Souls has more bosses, Bloodborne's bosses have a wide variety of forms and attack patterns. Many people would argue that the majority of Darksouls bosses are mainly strength built,with heavy armor or a large weapon to dodge. Though there are a few exceptions to this rule like, the rat bosses, the grave keepers, the majority of this holds true. Bloodbornes bosses vary from huge tanky creatures to tricky like the Moclash host of nightmares, where you un around in a mini maze and dodge his magick attacks, so speedy unrelenting bosses like the bloodstarved beast to where with out a good strategy can easily over come you with speed alone. Compared to darksouls bloodborne has a better variety of boss fights.