CS or SE? Which one is better to be a web developer?

I am going to apply for Computer Science or Software Engineering as my undergrad degree. Can you please tell me which one best prepares me to be a web developer? I love web developing, especially since it provides cheap services for many local business and their costumers. So, I am interested in pursuing my education in a major that help me to learn how to provide online solution and services widely. (web developing -mostly back-end development-, mobile application development, cloud computing, web 2.0 and etc).

I know it is a very basic question, But I tried to ask it from academic advisors of my desired college, and received cliche answers like: “follow your dreams” or “your goal maters more than your major”, Can you please let me know which major fits better my future plan?

(please mention your education and experience. although I appreciate detail answers, but short answers like this are desired: "I have studied CS and have X-year experience in web developing; CS -or SE- is more sufficient for you)

Thanks a lot