I'll admit to wearing lace up snake boots most of the time...........kind of a coward.
Have a pair of Muck Woody Armor that are kind of comfortable but HOT AS H$!!. Use them only for slipping on when a short walk is in store.
The lace up boots are Danner Pronghorn......very comfortable for snake boots but as with ALL GorTex lined boots they will leak sooner than you think if you use them a lot. This pair is 3 years old and has leaked for 2 of those years.
Chaps/gaiters have the advantage of being able to remove them as soon as you get out of the woods so your legs can cool.......as HD says though, if you want the added benefit of briar protection the higher the better.
I'll add this......I find that we are in the minority in the timber business in that most of the guys/girls ( Lots of female foresters ) don't bother with them.
Like I said......kind of a coward here.
Last thing......buy both. The boots will be expensive $100-200 depending on what you get.....the gaiters a lot cheaper.