Can you post a picture of the two skulls side by side to see size comparison?
I'll try to post the pictures but, for now, understand that the Smilodon skull is less massive than a lion skull. Also, our attention is drawn to the upper canines but, just as interesting, the mandible is light-weight and fragile looking. The lower canines are far smaller than any of the lions mentioned. On the other hand, Smilodon's gape was tremendous at 135 degrees or more whereas a lion's gape is closer to 90 degrees. It looks very much like Smilodon, dropped his mandible low so that it 1: wouldn't get broken in the struggle and 2: provided adequate room for the tips of the upper 'sabres' to be driven home. Related to this is that the horizontal crest on the back of the skull [nuchal crest] is much better developed in Smilodon than in a lion. This crest attacked neck muscles so Smildon likely had extremely powerful muscles on the back of the heck. He likely used these muscles to draw his head well back, probably at the moment of strike.
Powerful rear neck muscles combined with an incredible gape, likely meant that--during attack or threat--ithe canines were sticking almost straight out, just a little like a viper in full strike.
Some people have done experiments suggesting that Smilodon PUSHED his prey over; held it down; then worked towards the throat where he inserted his canines, perhaps ripping out his carotid artery producing brain death in a minute of two.. I think this scenario doesn't fit hunting strategies all of us have seen. A cat creeps as close as he can to an unsuspecting prey animal. No doubt this is what Smilodon did, too. Depending on the species, the cat tries to launch his attack from an ideal distance. Almost invariably, the prey animal detects the presence of the cat just before or during the initial phase of the charge. The prey animal turns to run, which means that Smilodon has no opportunity to 'push things over.' The charge is a dynamic process between hunter and hunted and usually puts our cat on the prey animals rump or rear flank This is exactly what we see when a lion or tiger attacks a large animal. and, from a distance, a Smilodon attack might have looked a lot like a lion attack.
Up close, however, something different is happening. Smilodon binds to the rear of the prey animal just like a lion or tiger. Also, like a lion or tiger, he bites the prey animal's rump or flank while trying to hold the animal. But here, Smilodon has an advantage, He cocks back his head, exposes his fangs and drives his teeth deep. The longer he can hold his prey, the more stabbing bites he can deliver. His canines are adopted for very large, powerful prey animals, so usually the prey animal shakes his tormenter off and runs or limps away. Smilodon follows, launching more slashing attacks depending on the opportunity. They prey, getting weaker and weaker, dies of 1,000 deep cuts.
My theory may be criticized on several grounds. Some people seem to thing Pleistocene America was more heavily populated by predators than are the most pristine parts of Africa today. This can't be true. Animal populations can't rise above levels determined, ultimately, by grasses and forbes. Even should it take Smilodon many hours to complete a kill, he was no more likely to lose it to an American lion than an Asiatic Lion is to lose his prey to a Bengal tiger. Others may say that my kind of kill would have fractured a lot of canine teeth but I don't think so. The 'bite' or 'stab' is directly into the largest muscles of the body i.e. the canines won't strike bone. Also, when he withdraws his canines, perhaps producing deep slashing wounds, he is pulling with, not against, the fibers of the muscle. Others say that the gape, as large as it is, isn't adequate for disemboweling a large ruminant like a bison. Maybe not but the cat wasn't aiming at the gut. He was aiming at the gluts. It wasn't a 'bite' but more like throwing darts into a dart board.
Then again, I don't know. I'm just looking at two old skulls.
