While the hero's gender in each game is different, there are obvious stylistic similarities. Don't think of Bayonetta just as a Devil May Cry in heels. (Well, at least until you play it.) Kamiya explains the game's relationship to DMC:
It sounds silly to be 'influenced' by your own creation which is Devil May Cry, but I can say that you may find quite a few common features, as my faith towards action games has never changed. However, I did not play DMC1 not even once while developing Bayonetta (I have played about half of DMC4 as part of my research study though). I have deliberately created Bayonetta from scratch and tried to make the game as original as possible, although there will be some similar elements to my previous games in there I'm sure, such is my unchanged faith in developing action games. Anyway, it's been eight years since DMC1, so of course I wouldn't create a game that hadn't progressed from those days! Of course, if there hadn't have been DMC, there wouldn't be Bayonetta, which has evolved from DMC.
What's more, if there hadn't been Hideki Kamiya, there wouldn't have been DMC. Or something like that.
Q&A: Hideki Kamiya on Bayonetta [GameSpot]