Underdiscussed (for me) is trail debris. The high Sierra, my typical hiking ground, is usually sand and gravel and I've learned too much dirt and gravel in my shoes chews up my feet. Gaiters are one obvious solution, mid-tops plus long pants another. The latter is what I typically do now, except day hikes.
Show/boot stability can be designed into low and high-tops, so the model is much more important than the height. That said, ankles are vulnerable to bruising and cuts with low tops, something not uncommon to our debris- and rock-strewn trails.
The good news: literally hundreds of models to choose among. The bad news: find something you love and it will be gone/overhauled the next season. Rinse, repeat.