Check the leading websites like Facebook, Twitter, and LinkedIn etc. None of these are using both “sign in” and “sign up” side-by-side onto their pages. Instead, they are using alternative phrases for “sign in” and “sign up”. Say, “log in” (for “sign in”) and “create account” (for “sign up”).
Some screenshots for further references. LinkedIn..
Another Pinterest page’s screenshot..
Since both of them (i.e., “sign in” and “sign up”) have the word “sign”, so users may get easily get confused and take wrong step. As a website owner we must bypass this and must not include any steps which may unclear to the users. So, either use “sign in” or “sign up” but not together.
This is actually a good practice and surely improves the site’s overall user experience. Making small changes like these may not have any huge impact however it’ll certainly make users happy.