It's probably too long to explain in one post, but overall Rachel has better speed, setups, damage and better tools in general. She might also be more popular judging by her appearance, personality, etc.
It's not just that,Rachel out of all the 3 characters appeared as a brand new character with the release of DOA5U,when she was super strong,so many people picked her up.Nyo appeared as the last dlc character in DOA5U,and Raidou is a LR character.Plus,out of the 3 characters,she is the one that in my opinion is the easiest to master.
Nyo is a really good character, Codemaster knows all the trickery. Rachel is just very easy to pick up, straightforward to use and shits out tons of damage. Raidou is plain garbage.
Well Raidou IS a copycat. Don't know if that would be the reason(probably isn't). I don't know much about the guy neither, but who knows, maybe in the future he'll get better?