You're referring to a road as gravel, that I would commonly refer to as dirt. However, it really doesn't matter, because both would be more efficiently traversed with a hybrid bicycle, due to the wider tires that will have more than enough width to roll over the gravel aggregates, but the tires will be thin enough to add less rolling resistance, between the road and the tires. This translates into greater speed and efficiency.
This is a gravel road (washboards included) that's quite amenable to hybrid or cyclocross cycling.
This is a rocky road with larger aggregates that would be more amenable to a MTB.
Mountain bikes are better suited to more challenging and diverse terrains. Such as in the example shown above. They were initially designed to decrease the shock of encountering the mountainous obstacles, that one routinely encounters when traversing mountain terrain.
Whenever human beings decide that they must make an improvement in function over whatever it is that is already being utilized, they usually do it out of need. The need to travel mountainous terrain, without all the bumping up and down movement, and erratic vibrations, surely preceeded the desire or need to have "greater control" of the bicycle. Control was the secondary benefit of the added suspension system to the bicycle, not the reverse.
Of course, a MTB will traverse the loose gravel more efficiently, but the OP doesn't want to travel the over whelming majority of his route inefficiently with lower gearing and fatter tires, where speed is sacrificed, and the entertainment factor is severely reduced. Once again, MTN bikes are better served where such obstacles as roots, rocks, boulders, crevices, and drops are encountered.
The simple compacted and smooth country road is the perfect domain for the hybrid. Quite frankly, that's where the hybrid best demonstrates its purpose. Wherever the hybrid is traversing the average dirt or gravel road, it is perfectly at home.
Can MTN bikes traverse the same types of roads?...You'll just bet they can. However, after the loose spots and washboards, they'll do it less efficiently.
MTB effeciency is best demonstrated on mountainous terrain, not on the smooth or compacted country road.
The MTB has made many improvements since the inception of MTN biking back in the late 1800's. The added suspension system is what really separates MTN bikes from the hybrid. This added suspension system has added weight, as well. The added weight increases the inertia of the bicycle. Inertia is a mass dependent entity, that is independent of vehicle's suspension system. The inertial effect of adding more mass will indeed aid in straight-line motion, but will otherwise hamper any change in straight-line motion, that's the just the fundamental concept of inertia.
Now on to the dog chase...
Cyccomute, I fear you've been watching too much of Ceasar Millan. While what you've stated here appears to be factual. I can personally attest to where your method would have failed miserably. Also, with stray dogs, its impossible to predict the outcome with confronting them. They could have rabies or distemper. In that case, they will be subject to any type of behavior whatsoever. However, with face-spray, it doesn't matter what their temperament may be or what their intentions may or may not be, all chasers get the same treatment once they've gotten within range. That teaches them not only to not chase you again, but quite possibly, it could avoid the next cyclist from being attacked, as well. They will learn to associate humans on bicycles, with eye and nose irritant.
Once while riding with my club many years ago. A pack of dogs began chasing us. We all thought that was weird because usually dogs don't attack groups of people. Anyway, we were all quite fast and manage to outrun them all, except for this one relentless dog. He must have followed us for a couple miles. We became curious as to just what this dog would do to all of us, if we just all slowed downed. The theory was... That if we slowed down, the dog would slow down, too!....WRONG!
As soon as he caught up to the last bike, he latched on to the rear wheel with the tenacity of a pitbull, over-turning one of our roadies. The dog refused to let the wheel go. We began to hit the dog with our air pumps. He finally released the tire and ran away!