One big advantage is that you are testing also javascript, including ajax calls. Web page can be pretty complex piece of code and not always is enough to test just plain html, you need to check how styles been applied, how page was rendered.
Selenium tests in this case I would rather call functional tests or if you like black-box testing, using Selenium IDE, tests can be recorder by somebody who is not developer, but knows how application should work.
Disadvantage is that tests can take a bit longer to run.