How is Gandalf the White a “significantly more powerful figure” than Gandalf the Gray?

Question

After his fight with the Balrog of Moria, Gandalf changed:

Gandalf was sent back as a significantly more powerful figure; Gandalf the White.
- http://en.wikipedia.org/wiki/Gandalf#Gandalf_the_White

What are Gandalf's new powers as Gandalf the White? What feats could he accomplish that he was not able to perform as Gandalf the Grey?

Answer 1

Eru sent back Gandalf with additional power, knowledge and wisdom. Prior to his return he would not have been able to rescue Theoden by breaking Saruman's spell and inspiring and leading the Rohirrim, nor face down Saruman, as originally Saruman had been the leader of the Istari and hence more powerful than Gandalf. Gandalf's barring of the Witch-King from Minas Tirith is another example. He merely aided Elrond's flood in keeping the Nazgul from Rivendell prior to his return. After his return he was able to directly face down and stop the Witch-King.

So Gandalf sacrificed himself, was accepted, and enhanced, and returned. 'Yes, that was the name. I was Gandalf.' Of course, he remains similar in personality and idiosyncrasy, but both his wisdom and power are much greater. When he speaks he commands attention; the old Gandalf could not have dealt so with Theoden, nor with Saruman. He is still under the obligation of concealing his power and teaching rather than forcing or dominating wills, but where the physical powers of the Enemy are too great for the good will of the opposers to be effective he can act in emergency as an 'angel'

From Letter 156.

Answer 2

Gandalf is overall more powerful as Gandalf the White. He is far more charismatic and has some limited foresight. He was able to defeat Saruman, breaking Saruman's power over Theoden and breaking his staff after the Ents took Isenguard. However, he was not all-powerful, seeing as the Witch-King of Angmar broke Gandalf's staff. Still, he is obviously more powerful, since, as Gandalf the Grey, he was defeated by Saruman, then he later broke his staff and cast him from the Istari and the White Council.

Answer 3

Gandalf was sent back by , I assume, the Valar, who sent him in the first place. This is because he had not yet finished his task, which was to oppose Sauron and save Middle-Earth from him. The fact that he was sent back as a white wizard, instead of a gray, would tell you something if you had done your research. The "wizards", or Istari, are ranked by color of their robes. Saruman has white robes because he is the most powerful. Gandalf has grey, because he is less powerful, but still one of the most powerful, possibly the second most powerful of the five. When he was sent back to Middle-Earth as a white Istari, he gained a significant amount of power that came with the rank, or the other way around, however you see it. So, it is expected that he would be more powerful after his return.