I used to be a semi-vegetarian. I would basically eat fish as well as fruits, vegetables, grains and beans. Sometimes a little cheese. I'd use olive oil and butter.
When I cut all grains (which contain insoluble fibers) and potatoes from my diet, all my digestion "irregularities" disappeared instantly! I truly believe that fibers are bad for you, except for the soluble ones found in things like fruits and vegetables.
I'd still eat a lot of fruits, vegetables and rely on fish and soy in different forms for protein and felt a lot better than I had for many years...
Anyway, a couple of months ago I decided to try going seriously low carb, since I had already cut so many carbs anyway. I was basically interested to see what it would feel like and if I would benefit from it.
So I went lchf (low carb high fat), kind of like Atkins. It wasn't that hard really, I just eliminated the fruit and upped the fat. Much more butter than before, about the same amount of olive oil and I also introduced cream and coconut oil into my diet. Yum! Saturated fats are not only tasty, but they are also good for you!
I've also started eating eco eggs and eco meat... And I feel great! I never feel heavy, bloated or tired after a meal even though I might be consuming "extreme" amounts of fats. I think that the reason why fats and meats are considered heavy foods is because most people combine them with a lot of carbs in the form of bread, potatoes, rice... And that combination will sedate you and may upset your digestion.
My energy levels are through the roof, and I'm getting crazy results at the gym; I assume that this is because a diet high in proteins/fats is naturally anabolic. I also don't have cravings or feel hungry, I almost have to remind myself to eat sometimes... I can honestly say that I am satisfied and never feel the need for chips, candy, pizza, chocolate or similar things.
I typically consume around 3000 calories per day, most of them from fat, and I'm certainly not gaining any weight. Just building muscles and getting rid of body fat.
I could still be a vegetarian, or even vegan, eating lchf but I've chosen to include more animal foods. This works very well for me...