How do I run two armies clashing against each other? What would I do to make it interesting instead of just killing over and over?

Small scenes within the overall battle. Have the PCs interact in one small part of the battlefield. Then narrate more of the battle, then have the PCs doing something elsewhere on the battlefield.

PCs have more important things to do than engage ballista fodder. Like taking out the enemy ballistas, or assassinating the commanders, or disrupting the siege train.

D&D is an absolutely horrid system to try and simulate large battles with.

You could give the characters specific missions that would help the overall battle effort. For example, killing an important figure on the opposing side or foiling a sneak attack from behind.

My DM runs the whole battles. They drag on for about five sessions sometimes.

Don't do it. OR if you do, count each unit as a swarm. Grunts AC 15 HP 80. Damage 6.  

Instead of just killing things, you need to give your players a defined mission.  Perhaps they have to get supplies to a particular unit somewhere on the battlefield, or they need to get a message to the general at the front.  If they have concrete goals you can use the chaos of the battlefield to put obstacles in their way.  Think of the battlefield as difficult terrain that needs to be crossed.  You can throw the occasional bad guy in front of them but you can also run stealth checks to see if they're noticed, or skill checks to climb over a barricade.

I was in a group that did mass battles as part of a Pathfinder campaign, and the system was campaign specific. And it was not fun. One player made all of the tactical decisions, and everyone else sat around and watched. And it wasn't satifying. 

If you are going to actually run the battles, you could probably adapt a specific boardgame to the purpose?

The best way to handle large-scale battles is to have them happen in the background with the PCs performing specific missions that influence how the fight goes: destroy an enemy supply train, rescue allies, assassinate a powerful foe, etc.

I ran a battle somewhat similar.  It was a pirate ship raiding another ship.  So I assigned two factions to each ship.  I gave them hp like 4 each, but the good guys I gave to hit roll of 10 or more where the bad guys had to roll 12 or more.  For every hit, lose a hp.  I then had the leaders fight the party.  I let each player run a faction.  No movement just a roll to hit or not.  The description was basic, there is fighting going on all over the ship.  Depending on how the faction fight went would sway the description.  The good guys are holding their own or you can tell the good guys are winning.  Or even if reversed, the bad guys are winning, their leader has really inspired them.  This could cause the party to focus on the leader and if he is taken out.  

But I used basic rules and involved the players.  They seemed to enjoy it.  No one was left out.  

An example - the PCs don't get involved until about the 4:30 point. Up until then it's big battle GM narration.