Web development wouldn't necessarily, in it's entirety be a full-fledged degree so much as it would be recommended to be called a certificate of multiple programming languages that specialize around the areas of XML, HTML, JAVA, etc. And then you'd probably be able to call yourself a website developer, not that it's no accomplishment, because it is. To the business sector, website programming is more like a tech degree, just depends where you're going. CS usually takes a little bit more work, if not a lot of dedication as any other field of study.
"Development" can be miscommunicated as research. In terms of website developer as a lesser degree, you are not entering the research field unless you want to be an assistant (if you're even lucky enough) to a Masters or PHD level graduate. Web dev. enables the graduate to learn how to create and modify and adapt to new web based languages and protocols, etc.
With CS, it's much more in depth with more advanced languages, allowing the graduate with CS to pursue more advanced career oppurtunities. So account for 'adaptability'. You can always try out for an associates in CS and do a tech degree in web development.
I think what people are tying to get at here is that if you want a quick trait and easy cash, do the web developer career, it will allow you to get your feet wet if you just don't feel like doing CS all the way, if any at all, but the classes may overlap with CS. Then again, it depends on the school you go to, months and years could be useful in acquired skills and knowledge or it could a waste if you're not sure what you want to do. Just depends on career goals and the way you learn like how efficient you are with math/logic and learning program languages.
Just finish what you start/started.