It is hard to compare the performance of the two styles of boots being discussed, without mentioning the context in which they will be used. In the case of the original post, used in some of the nastiest elk country you will find.
When carrying heavy loads, which is usually part of elk hunting, over uneven and difficult terrain, the value of a mountaineering style boot is worth the extra $100-$200 you might pay. Your feet will suffer far less fatigue over the course of a week-long elk hunt. As will your ankles, knees, and thighs.
The stability provided by the more rigid platform saves a lot of energy. When you have even a 20# pack on your back, in the type of terrain you will find in Unit 66, the amount of energy your body expends to stabilize your legs/steps in a lower quality boot, is very high. That is energy that could be used to hike and hunt.
Lower quality boots do not have the foot, arch, or ankle support of the higher end boots. Your foot, arch, and ankle still need to be supported, so your muscle groups work harder to do that. Thus greater fatigue to your feet and legs while wearing the boot without the more rigid support.
I understand why some would try to save the money. No need to spend money on luxuries. In the case of an elk hunt in the tough country of Colorado, high quality boots seldom fall in the luxury category.
When looking at the entire cost of an elk hunt, the marginal cost for an improved boot is pretty small, especially when that higher end boot will last you many more elk hunts than the lower cost boot. And, if it allows you to navigate difficult terrain more safely and with less exertion, your likelihood of success probably increases.