I have found that when I don't worry about what I eat, ratio wise, as long as it is in Paleo guidelines, I feel like I make more progress than when I stress over counting carbs and whatnot. So, which hinders fat burn more? Stressing over what I eat, when I eat, how much I eat, and how much I exercise or eating more carbs (over 50g a day).
As a side note: My ultimate goal is fat loss, but not necessarily weight.
I would go with stress. First of all I do not think it is fair to label carbs as bad, just like fat is not bad. One macro-nutrient can not be all bad. There are good and bad carbs, just like fat.
Besides that, if you do not have a handle of your stress, your diet won't even matter. For example, you could be eating a perfectly healthy diet, yet still be putting on weight.
Stress and sleep deserve more attention, as in my opinion they are much harder to control than diet.
My n=1 is definitely stress. I remember hearing Kurt Harris say somewhere than when his mind is in the right place he thinks could basically eat anything and not gain weight. I know my health problems didn't really start to flare up until I got hit with a bunch of non-health related stressors at once. There's definitely a balance to reach between eating healthy and not stressing a crap ton about eating healthy.
If you limit carbs (e.g. < 50g / day) that is a stress on your body. I'm guessing from the question that that is news to a lot of people. Paleo does not mean low-carb. Low carb is great for some people who are very overweight and/or have metabolic problems, and some people like it a lot, but carbs are far from inherently harmful. You should eat carbs unless you have a good reason not to. And, on the other side, you should not be stressed unless you have a good reason to be.
Depends on how bad the stress and how bad the carbs...
I wouldn't stress on the carbs unless you are sensitive to them - inflammation and/or weight gain. VLC (less than 50 grams carbs a day), and LC (less than 150 grams carbs a day) are for people who have been unable to achieve their optimum health with higher carbs. They are not for everyone.
I won't deny that there are some carb-sensitive people out there and they have to eat that way but first figure out if you are one of them. Not everybody is an Inuit (Eskimo) or has genes like that!
Some people even need some carbs to burn fat. The hubby and I accidentally started to do LC Paleo (got lazy making starches - was in the middle of winter and less produce anyways where I live) and some days of VLC. My hubby's waist didn't budge until we started increasing to some starches (bananas, tubers, and white rice) with every meal - then he dramatically had weight loss! Now keep in mind when we upped the carbs (20-25% calories from carbs) this is still a lower carb then Standard American Diet! We had both had better performance in the gym as well. You have to experiment and see.
Some people feel good in LC/VLC for a month or two and then start to develop new symptoms - dry mucus organs such as the eye, scurvy (wounds not healing properly, etc.). The Jaminets describe this in the Perfect Health Diet book and blog (I like to call Paleo 3.0).
Neither stress nor carbs are inherently problematic. That said, first, I'd tie the number of carbs you eat to your activity (which could vary day to day). And then second, do whatever you will do regularly ... I like Yoni Freedhoff's idea that you need to live the life you'll love, not the one you'll tolerate.
The comparison of stress and carbs = categorical error of the apples/oranges type.
Bad stress is to be avoided. As defined by Hans Selye and others. "Good stress" is the stuff that leads people to reach beyond their grasp, and thrive in the process.
Oh, and mediocre stress: "...lives of quiet desperation." Advantage: massive support group, known as Society.
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