Which pick is better for a service? Especially if I would like the website to resemble American style.
Gmail and Dropbox say: "Sign In or create an account"
Yahoo says: "Sign In. New here? Sign Up".
I believe shorter labels are preferable.
'Sign up' is shorter and, I agree with Dan, sounds easier than 'Create an account'. And indeed A/B testing can help to find the best solution in the context of your site.
One important thing to mention: I observed people in usability test being confused by the wording 'Sign up' and 'Sign in' next to each other. They're just too close and too easy to mix up. My learning from this was to use
Sign up | Log in
This article may be helpful to you: http://uxmovement.com/navigation/why-sign-up-and-sign-in-should-never-go-together/
From the article, relating to the optimal combination of labels for "signing up" and "registering":
"The ideal combination is one that allows users to quickly distinguish one action from the other without thinking. The more similar your actions are, the harder it is to tell the difference between the two. You can make your sign up and sign in faster for users to process by using action phrases that are completely distinct from each other. For instance, combining “Sign In” with an action phrase like “Create Account” or “Join Now” is much clearer because there are no similarities between the two."
I would choose whichever one fits with your service better. Both terms are commonly understood at this point so neither of them would detract from the UX. That being said, "Create an account" might better for certain websites (e.g. business, online shopping, anything centered around transactions) while "Sign up" might be better for sites that provide some kind of service. (Both Yahoo and Facebook use "sign up").
Ultimately though, I don't think you will gain or lose a lot of users based on the word choice; just go with what feels right for your site.
Personally, I think "Create an Account" supports better user buy-in. Yes it might sound like a bit more work but often you want people to care about what they're doing.
Conversely, "Sign Up" is very non-committal.
Ultimately it's about what you expect your customers to do next. If you want them to be engaged, you probably want them to have "created an account."
StackExchange has chosen to use the 'log in' single point of entry. When a user is known, he/she is logged in, when unknown, an account creation page is shown.
This approach is very appealing, because users are not bothered with an unnecessary choice.
"Sign up" refers to the website requiring a digital signature in accordance to the terms and conditions of an agreement. Sign is just a short form for signature. Providing and verifying an email address could be considered a signature, if that is stated in the conditions.
"Create An Account" is what you do after you have signed up. An account needs to be associated with a signature or profile, and often that can't be done until a visitor completes the registration process. That registration process may required them to agree to terms and conditions (that's the sign up part).
If you do not have any terms or conditions, then you just want them to register.
It's possible to allow a visitor to create an account without a registration process. Websites that offer anonymous services for example, and link the associated account with a profile threw visitor tracking methods.
"Log In" refers to the action of recording your entry into a security log. It implies that the activity will be recorded. Where as, the term "Sign In" refers to the action of authenticating a signature.
These are all old computer terms that have been so incorrectly used so many times on different websites.
Personally, "Create an account" sounds like more work than "Sign up".
This is a great candidate for an A/B test. Test them both and see which, if either, nets you higher conversion.