What would happen if Darth Vader fights Sauron?

A .nerd is born

If it came to an all-out war, Darth Vader would be able to summon up too much fire-power. Mordor would be defeated

But Sauron didn't become the Lord of the Rings  by being stupid. He'd invite Vader to visit El Casino de la Fatalidad  (on the slopes of Mount Doom, of course: Check the translation) where he'd be feted as a big spender. He'd be wined and dined, presented with promiscuous escorts of great beauty and rare talent, and honoured as a celebrity of supreme importance.

Then, when the poor schmuck had been completely sucked in, Sauron would present him with a ring -- the eighth ring of a very special set -- and when Vader placed it on his finger he would be lost! For this would be one of the rings Sauron used to enslave the elf lords and Darth Vader would become a ring wraith, forever in thrall to Sauron: A broken shadow of his former self.

But don't be too happy about it, for if Sauron decides to send him after you, where would you hide?

Hard to say since both are dead. 

Sauron wanted to rule middle earth, while Vader was well on his way to controlling the entire galaxy. Vader had a bigger army, laser weapons and a Death Star; gotta like those odds.