Tactics
Jez 10
The moon is indeed better equipped. More troops, heavy equipment, and so on. These cost money, food, sources of energy, water and these supplies have to be imported from planets, since moons are nothing more than barren wastelands.
Control the planets with the industrial infrastructure, removing the supply at its source, also giving a foothold to set up a blockade for other supply trains from other planets, which would take months of travelling just to reach here. That's how you win. Attrition. What you didn't account for is that your strength will be your downfall. You have more troops than you can self sustain from a moon. It's a mathematical inevitably.