two ways... 

1:) the tiers you sent were different.

2:) Your boosts weren't the same.

Power is not a good indicator of power / in that instance / for that application.

e.g. Studies give power. Econ, Assailant, and Inquisitor studies bring power, but have no bearing upon battle.

You can max out Cavalry, for example, for great power, but if you don't send any, that power indicates nothing.

You can have M's & B's of troops, which give power, but if they're not in play, that power indicates nothing.

If you won, you can go to the bottom of the battle report and click on 'Show more details' - lots of interesting stuff in there.

Sadly, if you lose, there is no show more details. When you lose, it's a complete mystery as to why.