What exactly determines the order in which units attack each other? What promped me to really ask is This Battle, where it's not like I lost or anything, but I'm a little disappointed that the opposing infantry was able to attack my Hussites (which have a base defend against infantry of 25...) while the defense team and city defenders did absolutely nothing. And it's not like my offensive troops just got attacked first, but none of my defensive troops came out to clean out the rest of the attackers. I nearly suffered as many losses as he did, despite having waaaaaay more power sitting in my city!

Is there some reason for this?

I believe the issue is that the battle in question is a plunder, which doesn't directly attack your city, which means that the primary troops that defend are the armies sitting idle at your city, and the city defense armies don't actually come out to defend unless they're the only ones there.
I'm pretty new to the game, though, so I might be wrong. Just speaking from observations made while I've been plundering people.