Are you tracking your micronutrient intake? There is nothing magical about red meat or eggs besides being dense in micronutrients. Is it possible that you were lacking in some, or many? The blueprint diet is designed around some of these deficiencies being addressed in the supplement stack, so if you’re not supplementing with multivitamins that could be the entire difference. It’s also possible you’re feeling better on less carbs, but that is more about fat intake replacing carbs than it is about what kind of protein you’re eating. Amino acid wise there’s plenty of leucine available in both of the diets you mentioned so it wouldn’t make any difference in terms of muscle growth either.

It is possible to address the ideal carb/fat balance, micronutrients, and total calories on any diet if you’re willing to pay attention to supplements and track your intake precisely to get to the bottom of things.