It’s all about the claws.

Although it’s been fun seeing pictures of some truly remarkable, gargantuan dog breeds in these answers (that Caucasian Shepherd is absurdly large!), I think the point of the question is being missed.

If there are Big Cats, why are there no Big Dogs?

All these mega-breed giant dogs are breeds. Hence, created by man, from a much smaller, naturally existing canine species. And they are all of the same species. The Big Cats are all of their individual species, and created by evolution. They gained their size in order to be the most successful predators possible in their hunting style (and in their niche), to survive. There are no natural canines that fit that description, to the same extent that the Big Cats do. The Timber Wolf is the biggest, and their size doesn’t come close to comparing with lions & tigers. And yes… there is a reason why there are no Big Dogs.

As Donna Fernstrom mentioned, it’s because of their hunting style. Felines use stealth and speed. Canines use endurance. But, there’s more…

Felines have pointy, razor sharp claws to “snag” a fleeing animal and bring it down.

And also able to disembowel by shredding with their sharp rear claws.

Canines have blunt, rounded claws.

Not particularly lethal, in comparison. They use their jaws to crush leg bones, injure muscle, harass, bleed out and eventually weaken their prey to the point that they can come in for the kill.

Extraordinary size would not be an asset for a canine’s endurance hunt. During the evolutionary process, there were no larger and larger canines born, who would survive better than their normal sized siblings. They reached a certain size, such as in the wolf, which was the sweet spot for calories burned during a hunt, and calories consumed. Anything larger was not proving to be an advantage. Marathon runners are not built like Arnold Schwarzenegger. And since their limbs (claws) were not being used as a major weapon, there was no need for their limbs to bulk up in the way that a lion or tiger is. They remain lithe, long distance runners, whose weapon is their jaws.

Felines, with their method of hunting, did bulk up. A stronger leg attached to those sharp claws could do more damage to their prey. And when they grapple their prey (using both “arms” to encircle or grab), stronger limbs are an advantage. When they slash, stronger limbs are an advantage. So evolution favored the stronger limb muscles. And stronger, bulkier limbs needed stronger, bulkier shoulders and a larger heavier body to attach to. So cats kept getting bigger, until they too, reached a sweet spot in size.

Because of this, felines attack their prey when it is at full strength, so they need extra size and bulk. Canines injure their prey, weakening it… then at the appropriate time, they kill. Size isn’t needed.

So it basically comes down to the claws, and the way each animal makes initial contact with its prey.

Dogs use their jaws to take down. They can’t snag with their dull round claws, and they don’t grapple their prey. In fact, unlike felines who have shoulder anatomy that allows grappling, or completely encircling an object with their front limbs, the anatomy of canine shoulder joints are not built that way. Canines can’t encircle or grapple with their front limbs. The mechanics of the joint are very much different, and is a very basic difference between dog & cat anatomy. Therefore, bigger, stronger “arms” didn’t help dogs. Limbs aren’t their initial weapon. And they burn lots of calories in a chase.

Cats use their limbs to take down. They snag and slash with their razor sharp claws. They grapple their prey. Bigger, stronger “arms” were very helpful. Their limbs are their initial weapon. And they don’t burn that many calories.

Both use their jaws to apply the coup de grâce. But first you have to take down the prey.

Both canines and Big Cats are at their perfect size for their species.

EDIT:

After answering the question above, I was asked about a specific “Big Dog”. Yes, there were pre-dogs and near-dogs that shared the Earth with what eventually became man's best friend. They don't get a lot of publicity. But they were a force to be reckoned with and were here for millions of years. But in the end, there was only one. So, who were they? And what happened to them? It's a fascinating story. If you'd like to know the prequel to the cat and dog story above, it's right here: Stefan Pociask's answer to What happened to the prehistoric Big Dogs?