It really depends on which foods are we talking about.
The variety of vegan foods is very large. There are several thousands of plants and vegan products that you may consume, they all have different nutritional (and calorie) densities.
I would say it always depends what you compare them with. When you do a comparison to omnivorous diet, do you count all the same (vegan) plants/products as a part of the omnivorous diet? Then they will overlap.
Watermelon and lettuce may have very low nutritional density, while seeds/nuts/grains/beans/avocado may have very high.
To answer the question whether vegans need to eat more food, I'd say it really depends with what you compare with.
You can be a vegan who eats only salads and raw foods OR a junk food vegan that drinks cola, eats fries with ketchup and (vegan) mayo. These are of course extremes, but you get the idea.
Eating a balanced diet composed of variety of foods is probably the best way to go, and I wouldn't worry much about the quantities.
If you are still curious, you can check out Daily Dozen app (both available for android and ios). There is a check-list of daily food recommendations for optimal health. It should give you an idea for the quantities.