This Troper did research into what the beasts are. According to the research, Raikou is based on a thunder spirit (the raiju (thunder animal or thunder beast)) which can take the form of several different animals, one of them notably being a tiger. Entei is based on the shishi, or stone lion. And Suicune is most likely based on the Kirin, or parts of it (the kirin being an amalgamation of animals, it only appears in areas ruled by a benevolent and wise leader, and can walk on water. Suicune constantly flees in the games, only facing you (in Crystal, Heart Gold, and Soul Silver) when you are either close to being or are a Pokemon Champion, and with how the games keep having your character praised as a friend to Pokemon, and the fact that one would have to be a good strategist (in the game universe) to be a Pokemon Master, well, that covers both portions required). The appearances are also uncanny