Galadriel's power

[The Might]

OK...

Case 1 - Galadriel no Ring, Sauron no Ring - it's pretty obvious from Inziladun's quotes that Lórien would have been lost in this scenario since even without the Ring Sauron could simply eventually overrun Lórien with all his forces.
I believe this also reflected in the words of Glorfindel:

`But in any case,' said Glorfindel, `to send the Ring to him would only postpone the day of evil. He is far away. We could not now take it back to him, unguessed, unmarked by any spy. And even if we could, soon or late the Lord of the Rings would learn of its hiding place and would bend all his power towards it. Could that power be defied by Bombadil alone? I think not. I think that in the end, if all else is conquered, Bombadil will fall, Last as he was First; and then Night will come.' ~ LotR, The Council of Elrond

So, eventually, Lórien would too fall as said above.


Case 2 - Galadriel has the Ring, Sauron doesn't

Now let's suppose that Galadriel kept the Ring and decided to use in battle against Sauron here's what would probably have happened:

In the 'Mirror of Galadriel', it appears that Galadriel conceived of herself as capable of wielding the Ring and supplanting the Dark Lord. If so, so also were the other guardians of the Three, especially Elrond. But this is another matter. It was part of the essential deceit of the Ring to fill minds with imaginations of supreme power. But this the Great had well considered and had rejected, as is seen in Elrond's words at the Council. Galadriel's rejection of the temptation was founded upon previous thought and resolve. In any case Elrond or Galadriel would have proceeded in the policy now adopted by Sauron: they would have built up an empire with great and absolutely subservient generals and armies and engines of war, until they could challenge Sauron and destroy him by force. Confrontation of Sauron alone, unaided, self to self was not contemplated. One can imagine the scene in which Gandalf, say, was placed in such a position. It would be a delicate balance. On one side the true allegiance of the Ring to Sauron; on the other superior strength because Sauron was not actually in possession, and perhaps also because he was weakened by long corruption and expenditure of will in dominating inferiors. ~ Letter #246 to Mrs. Eileen Elgar

I find this a very interesting quote, since it tells us very much about the chances of the three Guardians against Sauron. The problem is that Tolkien does not give a clear answer in any of these scenarios.
He merely explains how Elrond or Galadriel would have operated, and that they could not have faces him self to self, but does not say directly whether they would have been successful. It does however appears that they would have failed, due to the passage where it is said that it was part of the deceit of the Ring to show such dreams of great power. Still, I think that Galadriel or Elrond may have had a chance.

What also is interesting here is that although Galadriel seems to be more powerful than Elrond, he too is named as a potential adversary to Sauron, so perhaps the difference isn't that big as it may appear at first.

Ok, enough for now...