Web design and Graphic design compliments each other.
If you know how to do web design I think of course you need to know some graphic design, or else it's gonna be hard by just using the available graphics.
I think graphics designing is much better than web designing. Yeah I know graphics designing is a bit tough than web design but graphics designer get more demand and $$$ than web design. And at the it is all depend on your skill. If you don't skill than both field are gives you nothing.