A long time ago, before I free ranged, my chicken's eggs didn't look or taste that much better than store eggs. After I started free ranging, wow! They are delicious and have a rich flavor, as well as a dark orange yolk. During our long winters, if I don't supplement their diet with green feed, I can notice a difference in the quality of their eggs.
If you can free range, even in a limited way, I'd say do it. If you can't, I'd still try to get them more green feed. Things like grasses and dark leafy greens from the garden. Maybe you could sow some garden flats or pots to rotate into the run. Or plant grasses in the run and cover the sections with protective, wire-covered frames. A 2 x 4 frame with hardware cloth over the top works. Maybe some of the plastic garden flat trays that are really sturdy, open grids, that hold other plant containers, flipped over on the ground. Their design is sort of like a milk crate, but they are much larger and very shallow. Then, they could eat the grasses growing up through the openings, but not eat them down to the ground or scratch up the roots. A little chicken garden in your yard could have greens in it, that you could toss into their run, too.