Neither one, really.
Adequate nutrition is certainly important in egg production, if the hen is not getting enough to eat, she can't produce eggs very well, so she will lay less or stop laying. There is no ingredient in layer feed that "makes" them lay. I personally find my hens lay better when they eat a more "old fashioned" ration of whole grains and animal proteins than on layer feed. Also, the eggs are better on a more varied diet. Layer feed is what is fed to commercial hens, and their eggs are not all that impressive. I think storebought eggs taste nasty. Eggs from birds eating a more varied diet have a richer flavor and are more filling, to me.
It is possible that a change in diet has decreased your production level. Most greens are low in protein, and you want them to be getting at least 16% protein. You're already decreasing your protein levels by mixing the scratch (low protein food) with the layer feed, so unless the greens you are feeding are alfalfa or other legumes, they might not be getting enough. Try adding more protein sources to their diet.