Anyone that says calories don't matter has zero credibility. Anyone who claims calories are all that matter has even less credibility.
Focusing only on calories can get you in trouble. When you cut calories you usually see some short-term benefit. The initial results are alluring. But think of this like a metabolic credit card. You get some benefit in the short-run, but there are long-term penalties to pay later. Hunger, energy, and cravings (HEC) is your key to working with, rather than against, your metabolism.
If your HEC is in check then your metabolic system is balanced. And when it is, you're more likely to achieve a calorie deficit without even trying. So it's not about throwing calories out the window; it's about balancing the metabolism first, then attending to calories if required.
Food Quality Matters, Not Just Calories
Certain calories impact HEC differently. A doughnut and a chicken breast both have 250 calories, but which is going to make it more likely that HEC stays in check?
And yes, studies have shown that substituting equal calories of carbohydrate with protein leads to more fat loss, greater muscle maintenance, and less chance of weight regain. See the related links below for more detailed info.