Certainly meat tends to have much higher fat and protein density, and hence calorific density than vegetables, but the latter invariably have higher carbohydrate content (meat is essentially 0). Multigrain bread can have much the same calorific density as beef, and nuts are often considerably higher (admittedly, they're typically quite pricey per kg, though not more so than quality cuts of meat).
I've personally not observed any significant difference in the quantity of food I eat between vegan/ vegetarian/meat-based meals, though I very rarely eat meals that meat makes up more than a small percentage of. It's actually the micronutrients you need to be more aware of if you're on a strictly vegan diet, which are unlikely to make a difference in food cost (e.g. B12 supplements are about $9 for a gram, but that can last you months).