range attack works just like attack for meleers, it increase the likelihood to hit higher but the max hit is determined by your range STRENGTH just as melee strength works.
So the higher your range strength is the higher you will hit with the same gear, and the higher your range attack is the more chances you will have to hit near the top of your max hit guage. Increasing either will make you do more damage per second on average and get you more xp/hr on average, but only range strength will make individual hits have a higher possible damage amount.