Is a graphic design major worth more than a communication major?

I definitely don't think one is worth more than another! If you want to specifically work as a graphic / visual designer, getting a degree in graphic design is worthwhile. You'll learn the right tools and skills to land a job in that field. If you're looking to go into communications - media, corporate, etc - you may want to consider a broader communications field. Graphic design skills are useful in a variety careers, though. You can use graphic design skills in communications, marketing, UX, sales enablement, etc. If you don't specifically plan to go into a career in graphic design, it may be worth exploring a minor, or taking a few related classes.

My daughter graduated from UC Santa Barbara with a degree in Communications and was able to find work which was eventually unsatisfying to her. She later started taking courses in Graphic Design at a Community College and was able to find "odd jobs" designing pamphlets for local businesses before she had completed her GD coursework. She was able to get the odd jobs thanks to the extensive network of contacts and friends. As a bonus, she enjoys the Graphic Design work very much. To answer your question, from my daughter's story, the Graphic Design education seems to be more immediately employable, while the Communications Degree would require some sort of related specialization to bolster your CV.

A graphic design major is really a sub-set of the communications field, so it's more specific. You could pursue a degree in communications, or even visual communications, with a minor or focus in graphic design. Or, you could decide that you absolutely want to focus on graphic design specifically. The "worth" is VERY subjective -- depends if you work in government/civil service/education, vs. high-tech or private sector. Depends on if you're in an urban or rural area, etc. Good luck!