Both of the above are very important but do they get the recognition they deserve?
In my opinion, they are both important, but one of them is underrated. Graphic design is considered way easier than web design, but that's simply not true. Graphic design requires high creativity levels and attention to detail, plus the technical knowledge that website developers have. So roughly speaking is web design with some additional features.
On the other hand, web design is mainly the application of the knowledge you got from somewhere or someone, and it doesn't require any creativity. It does depend on the person though, if someone is more creative, they could be better at graphic design. But if someone is more into functionality and the more applicable part of the process, then web design is for them. They are not to be compared since both of the processes are crucial and very important, but since Graphic Design is not getting the recognition that it deserves, and it's always getting compared to web design, then we have to.
We also have to consider the fact that the client might be very picky and doesn't know what exactly he or she wants. This is the part where you come in; you have to understand what the client wants, and you have to create it based on their needs and desires. Your imagination and creative mind will be the solution. Meanwhile, the functional part is a bit easier. You add a button, you add a contact form, you make everything work properly, and you're good to go!
Think about a web page, or an app, without any "decorations" or without any visual design. Wouldn't that look plain and dull? It doesn't really matter how highly functional it is. If the user or the client finds it appalling, then it's not a success.
As a rough conclusion, everything depends on what you personally think and believe, it is also biased based on your own personal skills, but if we were to make a very general estimation, we would have to say that web design is underrated and that it needs a lot more recognition.