Garrosh knows the stories of the original Horde invasion of Azeroth, how they steamrolled the Eastern Kingdoms armies almost to the point of annihilation at the end of Warcraft 1:
However, he must also know that in what was Warcraft 2 we managed to push back the clans to the Dark Portal, seal it off, then even go beyond the Dark Portal and seal it off from there too. While in Warcraft 1 the original Alliance races had no love for one another, in Warcraft 2 they came together and forged the Alliance itself, so during WC1 the Horde had a major tactical advantage.
This was a time when the Orcs also had dragons at their disposal after enslaving the Red dragonflight, as well as permanent bloodlust from drinking demonic blood. Even so, we managed to beat them back eventually.
Now come WoD, Garrosh hopes to take over Azeroth against a currently strong and unified Alliance with (20-30?) years of improved technology, magic knowledge, freaking Deathknights and on top of that a new race which wasn't there in the original Alliance, the Draenei (won't mention pandaren, they're useless at warfare, and High Elves are replaced by Night Elves)?
Not only that, but he would also have to face the Azerothian Horde, comprised of Tauren, Trolls, Orcs etc... and Undead.
Between the Deathknights and Sylvanas alone they would probably have a field day raising every dead Orc to fight back against the Iron Horde.
And it's not even like the pandaria campaign weakened us severely or anything, we spent half our time there soul-searching and whatever, we each built a military base, and the rest of the time was sending task groups against different enemies and taking them out, this wasn't a years long war where we suffered crippling blows, unless you count Theramore which wasn't even pandaria related. Then as far as retaking Orgrimmar goes, we fought mostly a handful of Garrosh loyalists, and still managed to beat a Garrosh infused with Old God powers.
Now, to get to the meat of the argument:
In Garrosh's arsenal there would be no bloodlust (he wants the Iron Horde to be pure), no race variety thus only Orcish powers and intellect driving the army and its innovation, some new technologies from Azeroth brought back by Garrosh, which we already know of, no magical knowledge however, so it's gonna be Iron Horde shamanism vs Mages, Warlocks, Priests, Paladins, Shamans, with YEARS of experience in their fields.
On top of that, as mentioned before, he would face a fully unified Horde and Alliance on Azeroth, a Red dragonflight which would be on OUR side this time, and generally speaking a level of preparation which wasn't there in the original Orcish invasion of Azeroth, even though, back then, we managed to beat them back.
Not only that, but this time around Garrosh's new Horde will be fighting a war on two fronts: one within Draenor against the Draenei, now bolstered by Alliance numbers (and Horde?), and one with Nethergarde Keep's forces as well as whatever forces the Alliance and Horde leave behind to defend the Dark Portal exit.
This being said, historically speaking, how the hell does he hope to defeat us all? All he has are a few new toys that our Horde already has as well.