I am no military expert, but from what I have heard through army men and read, the big adavnatges are
1- You get to be on top, getting a good view of the whole theatre. You can much better see the enemy maneuvers.
2-The enemy has to climb uphill to get you out, and in the process, get tired and fatigued. The range of sight is also hampered of the enemy, because they cannot see far up.
3-You have a good range of fire,and because of point 1, you can control a supply line or crucial road link(like Northern areas war), you have the whole road under yourself, making it easy to stop supplies at will.