A couple things I've noticed:
1. Omen +morale is the one and only one skill for land-gain wars, I kill quick with these on, plus some other bonus, civic or tech I cannot recall that raises morale.
2. Start your assault near the end of a month, so that as the month flips, you get a morale boost, mid-fight, that works well for me.
3. Horses don't add **** to a siege, they have a value of zero. I didn't notice this until I realized my 10-stack of heavy troop was far better at sieges than my mixed 2 stacks of horse and foot. Duh.
4. It's random. So random that if you are screaming at the computer at how a 1k hill fort can hold out against your legion of Doom (with elephants! omg!), just resign and reload. It's totally cheap, but then again the system feels a bit out of wonk, so I do it when it's warranted.
5. Your opponents Loooooove Omen: Morale. I see it up constantly when I'm getting overrun by those pesky Romans and their 400k manpower.
6. Tech. For some reason, everyone is a higher tech level than me, even at easiest diff, and their are some nice assault/morale techs in there. This annoys.