First of all I like the overall way the fighting works. It is simple, quick, and doesn't require rolling dice. There is still the element of chance - with different levels of units and a random pick of units for use in your battle hand.
I don't think it makes sense however that you can win a battle even though you lost the actual battle. How can a military academy miles away from a battle win the battle after your army has been decimated? I can understand the extra scoring when attacking a city (even if you conquer the army in the city the citizens of the city might still defend themselves - and it takes a certain amount of strength to overcome and subdue the city itself).
When two armies are fighting in the open field it seems to me that the only way to decide the victory is to see who is left standing.
Having a military leader and military academies should boost strength in battle not strength after battle.
Here are some ideas for possible home rules (and changes the producer of the game can think about)
What if each military academy produced a certain type of veteran units - units that cannot be trumped according to the rules. Each player has a maximum of three cities and can build only one academy per city - you can get three types of academies: Army, artillery, and cavalry. When you build an academy you choose which units are made veterans. Or you build the selected academy based on availability (only a certain number of each type of academy is available)
The military commander can make obsolete one of the veterans of the opposition in each battle (or allow you to choose which types of units are made veterans).
This makes logical sense - because you have academies to teach a certain type of warfare, and generals who understand enough about fighting that they might use one technique in one battle - that either makes veterans obselete or improves the ability of your own units - and another technique in another battle.
Along with this, the philosophy technology should allow you to pick which great person you want - when you are studying philosophy, you would logically choose what type of philosophies you want to study - philosophy of war, philosophy of work, philosophy of trade... etc. Without this addition the philosophy card is a waste of time - if your strategy is military or production and you randomly get the rich old king with culture it is a waste of a city space and technology. Philosophy goes from a stupid investment to something that makes a lot of sense.
I'd love to hear about what others think of this proposed change to the fighting set-up.