My humble, uninformed, and strictly guesswork opinion is that the person with the more lush grass is taking proper care of it, including adequate (but not over-) watering, and supplying it with proper nourishment, such as appropriate fertilizer.
I once had a lawn in very sandy soil (in fact, the soil was nothing but sand) and it was brown, dead-appearing, and apparently beyond hope. I went to my local store for advice and to purchase the appropriate fertilizer, and the salesperson said "Why don't you try watering it first? Then you may not need all this expensive fertilizer, etc.". I went home, and watered the lawn (to the proper level), and within a week I had a lush, green, healthy lawn.