The two brands of laundry detergent I use most often are Arm & Hammer with Oxiclean, and Clorox Green Works. I don’t have as much of a comparison with heavy dirt, but through dance and long runs my clothes get plenty sweaty, and these do a nice job of making them fresh (and me presentable) again? Not sure that that’s more or less than any other brand does, though… So in that, I’m not sure.
Stains—I either put a little laundry detergent on the spot and brush the area in/under cold water—brush “up and out” don’t scrub the stain into the fibers—or else I leave the detergent to soak (usually submerged in cold water, or else I use Oxiclean spot-spray and cold water—I’ve had good luck with the spray with all sorts of fabrics, though I’ve seen others’ clothes get an unpleasant yellow discoloration from the product, so if you do try it, try with caution.
The pods—I’ve never used them—but I have a shared laundry room in my apartment and I know many of the other residents do use them, and use them incorrectly—they pop them into the liquid-detergent section of the detergent drawer instead of popping them in with the clothes like they’re are supposed to do… which means the plastic which encapsulates the pod soaps only partially dissolves, remaining as a weird translucent jelly-like gunk clogging the liquid-detergent well. Since this is my only first-hand experience with them, scooping out that leftover jelly, I am not a fan!