Well, it totally depends on your own field of interest that what you like and what you want to do? Both sound similar but different indeed. The both terms can be understood by their name 'Graphic designing' refers to designing on graphics and 'Web designing' refers to designing on website.
Both the field requires creativity and unique idea for attractive work.
With the help of Graphic's knowledge, one can create many forms like funny, emotional, sad and whatever person wants. Graphic designing allows you to free your hand on computer and make whole world surprised by your thoughts with the help of attractive and mesmerized designs.
Although, web designing is also same in the manner of decorating a website. But there is a point to note that for designing any website one needs basic knowledge of Graphic designing that mainly includes photoshop and corel draw. But Graphic designing needs no web designing knowledge.
Generally, Web designing contains coding which sometimes become hard to understand while graphic designing keep creating interest with colorful images. But, it doesn't mean that Graphic designing is better than web designing. Coding have always been an interesting and somewhere challenging task. Many people love coding as hobby and professionalism.
At the end, I would love to say that go with what you like not what people tell you in surrounding. Whichever course you choose, be best in that course.