Is it better to be Web Designer or Web Developer?
Web designer : he is the person who is responsible for creating the design for UI of the website. He is not concerned how the backed coding is done which process data but his work is to write code to give a website a appearance. He is also responsible for making logos or other graphic design. The language mostly used by him are HTML/CSS for UI coding. Photoshop/Corel Draw/Illustrator etc. for making graphics.
Web Developer : He is a person that works in shadow. i.e his work has nothing to do with the UI, he is responsible for back end coding and making its reaction for the user. E.g when user enter his info on web page his data is stored in database, making the website a secure version, controlling the traffic of website not letting it overload on many usage etc. The language involved is mostly HTML/CSS, JavaScript, Php, MySQL etc(There are many language where user can work).
Now since we know both of them are required to develop a website, so asking which is better is not a fair question. When a team is created to handle a web project it will have equal contribution of both employees. Developer cannot submit a project if it does not have a appealing UI for user to use and designer cannot submit the project if only UI is good and the website dosen’t do anything useful.
So now you should decide on basis on where your interest fits.