zetor, Out here moss is a major player. You have not told us where you have the problem. Household bleach and water (cup or less to gallon) and a bristle brush will remove and kill it on concrete and wood. The store bought stuff is expensive and I have not found it any better. On roofs some swear by powdered Tide (w/bleach). The problem is the delivery system. I jury rigged a long handle to an empty gal milk bottle with holes. On a ladder is was possible to roll the bottle around to spread the powder. My roofs are very steep and I would not try to walk along the ridge. After the powder is spread rain will distribute the powder and the moss will die. After summer dry out the dead "moss mice" will roll into your gutters. This is not thought to be environmentally friendly. Sun will kill moss. The north facing roofs are the real problem.
If you mean grass vs moss. It gets expensive fast. Pros spray some kind of "mojo" juice. I have not had it done, but my neighbors do. Their grass is near perfect and mine is not.
The main problem is acidic soil which promotes moss and low spots. The Ph can be tested by a landscape co. Lots of "sweetening" is done here by spreading tons of soil amendment to change the Ph. Proper Ph allows the grass to squeeze out the moss. It gets real expensive.