[Boromir88]

Bricho and Esty both bring up two good points. As I'm sure it wasn't just for one soul purpose. There were several reasons for Gandalf to save Faramir's life over helping out in battle.

Esty talks about one of them. After Denethor's death Gondor was sucked into a political vaccuum, just imagine what the soldiers had been going through? I mean they see their great captain and Denethor's heir (Faramir) brought into the gates severely wounded. Denethor refuses to step out of his hall and lead him Men as he is asked this very thing:

'The first circle of the City is burning, lord,' they said. 'What are your commands? You are still the Lord and Steward? Not all will follow Minthrandir. Men are flying from the walls and leaving them unmanned.'

'Why? Why do the fools fly?' said Denethor. 'Better to burn sooner than late, for burn we must. Go back to your bonfire! And I? I will go now to my pyre...~The Siege of Gondor

When Denethor showed no intention on stepping out and leading his men Gandalf assumed command of the City. When Gandalf had to later attend other business he places Imrahil in charge. Then after the battle, after Denethor's death, Faramir is the Steward of the City, but he's still sick and is in no health to rule, so again Imrahil is given temporary Stewardship until Faramir is better.

So there were definitely political reasons, as Denethor's death (and even before his death as he refused to provide leadership), caused a big political vaccuum in Gondor. For Faramir to die along with him would be even a bigger vaccuum.

Despite all that, I agree with Bricho that it wasn't all about politics. First I'd like to say it's not that Gandalf chose Faramir over Theoden...Gandalf had no clue Theoden was going to die...he just knew if he saved Faramir than many more would also die. But we're talking about a war here, many more are already dying. At least everyone in War expect that they may not make it through. With Faramir's life on the line, Denethor had no right to take it. Here's what Denethor says about him burning himself and Faramir:

'To my pyre! No tomb for Denethor and Faramir. No tomb! No long slow sleep of death embalmed. We will burn like the heathen kings before ever a ship sailed hither from the West. The West has failed. Go back and burn!'~The Siege of Gondor

Now we aren't sure exactly who Denethor is talking about here as the 'heathen kings.' But as silly as a concept as it sounds, the Numenorean Kings had the power to command their own day of death. They were allowed willingly to decide when they wanted to die (as we see Aragorn does). According to Denethor he has this right to command when he dies, as well as when Faramir dies, but as Gandalf points out he does not:

'Authority is not given to you, Steward of Gondor, to order the hour of your death,' answered Gandalf. 'And only the heathen kings, under teh domination of the Dark Power, did thus, slaying themselves in pride and despair, murdering their kin to ease their own death.'~The Pyre of Denethor

Here we see heathen kings again, and according to Gandalf these were King's under the 'Dark Power' who committed murder. Therefor, this is not Denethor rightfully ordering the hour of his own death and taking that of his sons. This is Denethor, who has no authority to order when he dies, and certainly no authority to commit murder.

Just as a point of interest, Gandalf says the heathen Kings slew themselves and their sons in 'pride and despair,'...hmm it's interesting that Tolkien applies these two words to Denethor:

Thus pride increased in Denethor together with despair...~Appendix A: Gondor and the Heirs of Anarion; The Stewards

Not only was it political, but I think Gandalf thinks of it as a moral obligation. Gandalf, I've always seen as the top of the moral ladder, he is the one that is there to point people in the right direction when they go astray. As some examples, when Frodo wishes Bilbo killed Gollum, Gandalf instructs Frodo about the importance of Pity and Mercy. It is that very Pity and Mercy that made the quest succeed and Frodo's life was spared. When Aragorn proudly goes up to the hall of Theoden and tells Hama he is Elendil's heir and he should have power over Theoden's orders. Gandalf holds Aragorn and tells him a King will have his own way in his own hall. So Gandalf has always been also this figure of justice, and this moral compass. Therefor, I believe Gandalf found it his moral obligation to try to save a life that was about to be wrongfully taken, over those who had through free will gone into battle.