The obvious type to add into the language was bool. But unfortunately, plenty of code was written that included bool in other shapes and forms. Recall that support for a boolean type was added only in C99.
So the C language committee had no choice but to pull out a reserved identifier for it (_Bool). But, since the obvious choice of type name is still the same, stdbool.h was added to allow users the obvious name. That way, if your code didn't have a home-brewed bool, you could use the built in one.
So do indeed use stdbool.h if you aren't bound to some existing home-brewed bool. It will be the standard type, with all the benefits that type brings in.