Software Engineering opens way more doors then a specific web development degree. So you would have a wider job market apon graduating with a software engineering degree. The key aspect of software engineering is that you learn how to manage software development projects from having maintainable code, working with teams and source control, creating and executing release schedules and the like. Software Engineering however is a 4 year degree as opposed to a 2 year web design degree. Plus if you study web development languages\concepts (Javascript, Flash, Web Services, Apache\IIS, etc) while enrolled in a 4 year software engineering degree and take a few writing and art classes to boot, you'll be a very strong web developer candidate.
Computer Science focuses more on theory of software and hardware systems. You'll learn material in a very broad fashion with classes ranging from digital hardware design, computer programming, database management systems, operating systems (and how they work) and ideas about algorithms which are ways to solve problems. Plus there are a lot of elective courses in CS like AI, Virtual Worlds, Information Retrieval (Search Engines), Natural language Processing (How to get the computer to understand human language), etc. If you go for a master's then you should definitely pick Computer Science, a MBA would be better if going for a master's with Software Engineering.
|