I'm going to be blunt and start throwing facts around, mixed with history, and evidence to support the argument. Because I just don't see how Ponies could win.
I believe that Humanity would win. Why?
Humanity is a race of predators, and, no matter what you or anyone else says, are still a species with predatory instincts. Now, given that the Human race does fight it self on many occasions, we are not United. That would some what weaken us, because of how volatile these differences can become, eventually boiling over in to war.
Ponies however, don't have this trait like Humans do, giving Ponies a 'Unity' Edge against the human race.
Humanity is also capable of thinking on a more violent basis then a pony can. How? A example would be that of Germany in World War one, and World War two. Germany could hold its own against any country that tried to fight it, and it always seemed to gain a strategic edge over the country Next to it, tell some one stronger got involved. Once that happened, they still managed to hold out for a fairly long time tell the invasion and fall of Berlin, and the death of Hitler. Not only that, but humans are also issued weapons capable of mutilating another creature, wither or not its a bayonet, or a submachine gun.
Also, considering that Ponies don't have opposable thumbs, they would NOT be able to use a Rifle or any gun effectively unless said Pony was a Alicorn or a Unicorn. But not only that, but you can't exclude the fact that Humans, while fragile, can still be as strong a brick wall if they were introduced to the proper situation. If a Human is enraged, simply teleporting his gun or knife, or both, away wont help the pony, the human well simply snap the ponies neck and take his weapon, or use his bare hands, user's choice.
Humanities Militaries mostly range above 2,000 troops. If you factor in Indonesia, Russia, the United Kingdom, the United States, China, and Brazil, the military power is fairly vast.
Mankind, has also made war in to a art, killing with the perfect blade or gun is a merit amongst mankind.
Not only that, but tasking a Unicorn with taking down a Tomahawk missile, when he has no idea what a Tomahawk missile is, nor does he know what one looks like.
Add the fear factor that a pony would get seeing a tank role over a hill or his friend, then have the gunner starting unloading towards him with a 50. caliber machine gun mounted on top of the tank. Wouldn't you be scared? of course the fear factor counts for Humans to, but its not always as severe.
Add in Chemical and Biological warfare, and there is another edge to the human side so long as the humans are prepared to try to clean the chemical waste, and have the proper equipment to send troops in to start carving out the survivors.
Wither or not Humanity would take pony kind as a slave depends on wither they just kill the ponies, or if they let them live as prisoners, or they would occupy the area of population, and the ponies would have strict curfews and laws enforced on them by the occupying force.
A Thermonuclear Warhead could easily turn a Alicorn to dust, due to the vaporizing effect it has within a certain radius of its impact and detonation point. A pony species, no matter what they do, can not defend against this tell they know what it is, and its likely that they wont be that aware of the effects tell its to late to react. Not only that, but there is also the Normal missile launcher.
Canterlot is standing off the side of a Mountain, with a lot less structural support then you think.
A few well placed Missiles or rockets could easily take the city off the side of the mountain drop it a few thousand feet on to the ground. Or the humans well bombard the city with Missiles, Rockets, and bombs tell they manage to make it submit, and possibly the city well fall off the side of the mountain anyway, or the buildings well give way to the pressure and the damage and collapse.
A Alicorn Princess MIGHT be able to fight. Might. Magic is not the strongest. Maybe there shield can protect Canterlot for a minute or two before it gives away to the missiles.
If you factor in the usage of Bombers and aircraft, mankind has Another edge. Human War machines such as the F-22 Raptor, or the F-16 can be used to unleash a torrent of Bullets and missiles on to Civilian centers, the Pegasus race, Alicorns, Floating cities such as cloudsdale, etc.
a Boeing bomber can drop a bomb from the sky and have it land on its target with ease, because of its shear size and capabilities as a bomber along with computer assistance. A Apache or other attack helicopter such as the Le Tigre can easily put down the Pegasi and the Alicorns, Unicorns, Earth ponies, while also being able to damage a civilian center severely before rearming.
While a Pegasus and a unicorn have favoring factors, it still wont help them more then you think. Humans have the infamous 'Sniper' on there side. Because of the long range capabilities of a Sniper rifle, It is not hard to Kill a few ponies and weaken the defenders or attackers, and help to burn them down to nothing but a few bodies.
A human with a knife, is in some ways, more dangerous then a human with a gun. How? Let him or her get up close, and you get shanked repeatedly, or just plain out stabbed. Once you get stabbed, there is little to be done but to try to kill the thing that shanked you, or just sit down and die.
the Flame thrower is a marvel of war. It can be used to clear out buildings, block paths, kill, clean up bodies, etc. they can easily just turn ponies to nothing.
A air invasion would be obvious, but there would be little a pony could do to stop it if he was grounded, like a unicorn of Earth pony. Pegasus and Alicorn ponies might be able to do something to fight, but if the paratrooper has a gun with him, witch I bet he does, he could unload in to the Pegasus or Alicorn and still keep his descent from turning to a free fall.
