Mission rewards at the end are based on the level of the mission. Increasing the level/difficulty of the mission will increase the level of the reward.
You can only get items with light stat from missions that are level 20+, strike playlist, raids, and the crucible. They will not appear in regular strikes or missions under level 20.
You are correct about the more enemies meaning more chances for engram drops, but you could also just farm explore/patrol mode for engrams instead of missions.
I'm pretty certain the highest rarity non-level 20 items only go up to blue quality, and blue engrams drop consistently from level 1 to level 20.