The theory of "low carb diets" is that they reduce your appetite, resulting in fewer calories consumed.
This has been my personal experience. I started eating "low-carb/high-fat" last September and just crossed the -60 pounds mark. I still marvel at how I'm just not very hungry most of the time, even after missing meals or exercising for several hours... or how I can, indeed, go ride my bike vigorously for a few hours before eating any breakfast.
I haven't counted calories at all, so from an objective sense, I can't give precise amount of wha I used to eat compared to what I eat now. However I'm certain I eat less from the mere fact that now I often miss meals (from not being hungry enough to bother) when before I might even eat 2 lunches, and snack much less than before (evidenced by the fact that I don't buy snacky foods much any more - when for example I was subscribed to Amazon to have boxes of KIND bars delivered to both my home and office). One of the best parts is that I can now take long bike rides after work (I've been a bike-commuter for a few years) and not have to rush home to eat dinner from crazy hunger.
I believe the theory about low-carb and hunger is that carbohydrates stimulate insulin production. This causes cells in the body (fat and muscle) to take up blood glucose more than they would otherwise, thereby lowering blood glucose. This dynamic system has delays, so blood glucose will drop below the "normal" level and as a result you get really hungry in order to raise it back up again. As a result, you either eat more or feel lethargic due to lack of energy. This may explain the need/desire to snack between breakfast and lunch and after lunch in order to stave off the fatigue and "crash" that most people experience at these times.
Some people go a bit nuts when I say I can eat as much as I want with this way of eating and still lose weight - as if they think I believe I'm violating the laws of physics. But the reality is that of course I'm obeying the laws of thermodymics - it's just that when I eat a diet low in carbohydrates, I just don't want to eat very much. And how can that be a bad thing? I'm getting fitter, feeling better, and all without being hungry or otherwise suffering.