So this is your new angle Andreas? Alaunt is your buzzword for the month?
You know, we've had our problems (big problems), but I have missed you. I've always maintained you make dog forums better, way better. I haven't been posting on any dog forum regularly for a long time, because they're just boring without you. Lol. 

I would say the two types of dogs being discussed here, the divergence, is really quite simple. 
One coincides with the domestication of sheep and goats, and one the domestication of cattle and swine. These respective domestication processes naturally resulted in different evolutionary directions for the dogs which were pivotal players front and centre in said domestication processes.

You see a heavier boned more stationary watchful guardian has evolved alongside sheep and goats (since they primarily require protection), and a lighter more agile gripping dog has evolved alongside cattle and swine (since they primarily require control). 

It needs to be understood that man didn't domesicate things like some all knowing genius, in all cases it kind of just happened, gradually. The domestication of dogs in the first place wasn't from man taking wolf pups from a den and raising them as his own (a ludicrous concept), it was from wolves lingering and scavenging around human settlements and gradually evolving to be more tolerated and thus more successful scavengers. This is how the dog was "domesticated". It's really an animal which evolved to suit an available niche. The humans involved were mindlessly present, even victimised, rather than all knowing and in control of the whole thing. 

As dogs got closer to humans, more and more dog behaviour rubbed off on human culture. It was in fact dogs which domesticated herd animals for people, and this happened because it's naturally what wolves do. Humans naturally just go out and look for prey animals to hunt, but wolves manage a territory full of prey animals, and they know every animal that lives in it. They watch them and follow up on them and analyse their scents and learn their patterns and etc, and basically they are ranchers with a ranch full of herd animals that they farm and manage carefully, harvesting the odd one when the time is right. Dogs taught us to farm animals, they've been doing it for millions of years, we started 9000 years ago, after partnering with dogs, coincidence?  

We took some convincing too. At first dogs were tolerated at human settlements grudgingly. They were pesky vermin hanging around, getting kicked and punched and cursed and told to get lost. But they persisted, slowly showing their worth, at first with truly the lowest of all lowly jobs - eating feces. Yes that is how dogs started to first impress humans. This can be seen today in stone age man/dog relationships like that seen in tribal papua new guinea. What you see in papua new guinea is basically a window into the past, around 30 000 years into the past, in every way, but including the man/dog relationship. You can see it's beginnings in this primitive culture.

They would eat their waste, and their garbage, which was handy, and they also killed or chased off rodents and snakes and etc etc. They started to learn to alert humans to intruders, invading tribes and predators, and finally started to be tolerated to come along on hunts. They would have been disruptive to the natural hunting techniques of humans at first, but gradually humans would, over time, recognise the value in their strengths, like their sense of smell, their speed, etc. 

It took time for dogs to convince humans to see them as hunting partners, rather than freeloaders tagging along, but once they gained that trust they slowly started transforming the way man hunted game. Man would start following his dogs out to herds which the dogs knew were there, and the dogs would pick off weak individuals and harrass them (just like wolves) until the men caught up. Man started getting more in tune with and knowledgeable about the animals in his domain, and dogs started learning how to use man to their benefit as well. Wolves herd naturally, which many people don't know, they'll run herds and separate herds and drive individuals where they want them to go. Dogs soon learned to herd more flighty animals back towards humans to be killed, which wolves had always done with their own packs. 

Herds of animals started going from wild to semi-wild. They're wild and free, according to them, but according to the man/dog alliance, they belong to them. 

The herd animals started to unknowingly evolve to fit this new arrangement. 

Later certain human cultures would focus more on either sheep and/or goats or cattle and/or swine, and when they did this their dogs started to change in accordance with whatever kind of management these different animals naturally called for. 

With LGDs we see the dog's response to the evolution of sheep and goats, today some LGDs might work with cattle, and in the past (and in primitive cultures) proto-lgds worked/work with cattle and herded/herd them around, but really LGDs are adapted for managing goat and sheep. It became beneficial for them to stop "hunting" the goats and sheep, and instead put them at ease by being slow and calm, wandering amongst them as a protector. Alternatively, far away a different approach to sheep was taken up by the herders and collies, controlling them and running them around. Different ways to deal with these animals but both worked. 

Meanwhile dogs were evolving along side the development of cattle and pigs as well. This stayed more like hunting for a much longer time, and still is hunting in some parts of the world with wild or semi wild cattle and pigs hunted by man and dogs in the traditional pre-domestication way. This other family of dogs is related to lgds but on a deviated path. Some might even guard livestock to a degree but this holds much less importance as their herds can guard themselves pretty well, instead their primary function is controlling and subduing these unruly beasts to make them reasonable for humans to interact with.

Very different roles, pushed the "mastiff" "molosser" "alaunt" or whatever you want to call it in these 2 deviated directions.  

As a result now the most extreme specialised LGDs are practically useless as hunting dogs, and the most extreme specialised gripping dogs are practically useless as guard dogs, but more primitive varieties of each are still somewhat well rounded to varying degrees.