Sign in vs Log in
In “Homepage Usability”, Jakob Nielsen (together with Marie Tahir, 2002, p. 53) recommends the use of “sign in” / “sign out” over “log in” / “log out”. This is empirically based on a survey of several large-scale websites and thus supports OP’s “more common” argument.
Furthermore, I second @Dan Barak in that you should use “Register” or “Join [your-service-here]” as opposed to “sign up” in order to avoid unnecessary confusion. (I cannot recall whether Nielsen and Tahir had any recommendations regarding this issue, though.)