Well I find that it's a couple of things that contribute to falling or not. The first being after countless hours of bush whacking and almost falls, you build strength in the core muscles that help you keep your balance as well as step high to avoid objects that might trip you.
I like the high heel because it is better for really steep slopes. It allows you to dig in and get a good foothold. The foot angle also takes stress of your mid foot. My feet feel better after a long day of high heel boots than flat.
Now with that said, there are many people I have come across or work with that just can't wear a boot with a heel. wearing a boot with a heel can actually be painful until your feet adjust, many people just give up before that happens. The tendons in your arch get tight when you wear flat shoes (tennis shoe, hiking boots), then you put on a pair of high heel boots and the tendons get stretched and your feet hurt. just like any bother muscle, with time, they stretch and the pain stops. Usually takes a couple weeks of progressively longer time with the boots on.
I would say most of your tripping is do to boot weight, making it slightly more difficult to step high, and possibly age.
With all that BS said, I must confess, I fall a lot. Regardless of footwear, if im not on a groomed hiking trail, I'll be on my ass before the day is done.