In “Homepage Usability”, Jakob Nielsen (together with Marie Tahir, 2002, p. 53) recommends the use of “sign in”https://ux.stackexchange.com/”sign out” over “log in”https://ux.stackexchange.com/”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.)
While I don’t have a very strong opinion here, I would bear in mind:
- Sign In and Sign Up are quite close.
Users might click one instead of the other sometimes.
Either you make the difference more evident by location or graphics, or you could also use “Register or “Join” instead.
- Make sure you stay consistent with the log out vs. sign out.
I think that this article about the “Sign Up” button is interesting, the author changed the “Sign Up” button to “Try it Free” and clicks increased by 212%.
His thesis is that the standard “Sign Up” buttons don’t work because “they ask for blind commitment” and “do not offer any value”.
Visitors also “see common elements repeated on many sites” and “they begin unconsciously ignoring those elements (aka “habituation”)”.
- Tie it to your product. If you have a SaaS for trading bitcoins: “Start Trading Bitcoins.” If you have a marketplace for artists: “Start Selling Art.” This helps prevent the button from being overlooked.
- Give, don’t take. “Get Access” and “Sign Up” both lead to the same thing, but one makes the visitor feel they’re getting something, while the other doesn’t.
- Compel people to act. Use action verbs such as get, start, and try.
Of course there are many variables to consider (what kind of website is yours? Changing the label of the button increases clicks, but what about new subscriptions? etc.) but it may be worth having a look at it.