I originally went Paleo and very low carb at the same time, and initially I felt great. Lots of energy, better mood, reduced appetite, and i lost about 25 pounds and 4 notches on my belt. I was strict low carb, about 25g per day. During this time I was probably burning fat.
But one day, I stopped feeling good, mood and energy declined, had digestive issues, and stopped losing weight. It literally just started happening one day though I hadn't changed diet or anything else. Meanwhile, appetite increased and I often had the munchies. I consciously added back starches, very carefully, primarily sweet potato, banana, plantains, occasional fruit, and almost exclusively post work-out. I started to feel better, not as great as when I was burning fat, but better.
After adding back starch, I gained a few pounds back, but got a little leaner according to my belt. I am not lean or ripped by any measure, and track my diet primarily by my belt. I thought it was interesting that I gained weight but got a little thinner on starches. I had such great success going low carb that I am very reluctant to eat lots of carbs, this might not be a bad idea to try but I just have trouble doing it. I still completely avoid gluten and bad oils, and only very occasionally have other grains (i.e. corn on the cob).
I suspect that my metabolism/digestion was broken in some way when I started, and the period of very low carb fixed it, and now carbs have a different effect on me than they did. Also avoiding wheat has had a major positive effect while some other starches seem relatively harmless. I still have a zero-carb breakfast most days, typically coffee with cream and two eggs. But I make a point to have "good" carbs at least once a day, either sweet potatoes with dinner, or occasionally berries with creaor yogurt for breakfast.