Since no one has bothered to answer yet I will be the one to answer this first.
I prefer the Big Mom Pirates over the Whitebeard Pirates and the Beast Pirates because I love their great variety of designs, powers and personalities more diverse than especially the Whitebeard Pirates, of their twisted fairy tale theme and designs, of them being a ruthless crew but yet much more ambigiously grey than the Beast Pirates and Blackbeard Pirates with them ruling over a country and them being presented as having genuine care for their country and people in Moscato and Amande's cases, and their genuine love for each other as siblings.
I also like how creative they can be with their devil fruits and powers such as Cracker's biscuit soldiers filled with jam, Mont d'Or's books and illusions, Opera's burning cream, Perospero's candy pieces of art and everything that Katakuri does, etc...