The empire probably wins army vs. army.
However, they would still have Sauron to deal with ... and so long as the ring exists, the most they could accomplish is to destroy his physical form. He cannot be "killed".
Details:
Orcs, Haradrim, Easterlings, Variags, Trolls, Half-Trolls, Wargs, Uruk hai, Black Uruks: Still biological beings. No amount of swords or brute strength can cut down an AT-AT or deflect blaster fire from the myriad of empire troopers or tanks. In addition, the empire has no need to even get close. This can all be done outside of striking distance of Sauron's army.
Mumakil: Easliy cut down from a great distance by AT-ATs, TIE bombers, TX130s etc
Fell Beasts: Easy pickings for Tie Fighters
In the end, the Nazgul would still be alive, but helpless to do anything about the empire. While it cannot "kill" them, fire is their weakness, and the empire can drum up plenty of that with no problems. They would have no choice but to flee.
The dragons would be the only forimdable enemy ... but considering how quickly the empire would wipe out the rest of the army ... their entire force could focus fire on the dragons and they would fall rather quickly. The underbelly of dragons is vulnerable to attack. Smaug was an exception because he had lain on the horde of gold for so long that gold and jewels were encrusted into his scales protecting his underbelly. An average dragon would not have that benefit.