Pathos

The last paragraph of Churchill's speech is clearly a rousing appeal to the audience's emotion. You don't refer to "monstrous tyranny, never surpassed in the dark and lamentable catalogue of human crime" (24) unless you're trying to evoke an emotional response.

Okay, you could try to use something like that if you're going for logos, but then someone's going to ask to thumb through the "lamentable catalogue," and things could get weird.

Even in the less exciting parts of Churchill's speech, he uses the dramatic situation of the war as the backdrop for his drier parliamentary business. For example, when he talks about having to make a war cabinet just about overnight, he says, it "has been formed of five Members, representing, with the Opposition Liberals, the unity of the nation…It was necessary that this should be done in one single day, on account of the extreme urgency and rigor of events" (5, 8).

Remember that Churchill isn't just addressing his colleagues as their boss for the first time; he's telling them about major changes in their leadership that have happened very suddenly and quickly. A lot of them were still loyal to Neville Chamberlain, so throwing in some gentle reminders about the clear and present danger would give the audience some perspective.

Then there's the end of the speech, whose purpose is to get people amped up and ready to wage them some war.

Ethos

Churchill was already a colorful and well-known figure in British politics who'd held lots of roles in government and the Navy. He didn't have to spend any time introducing himself. But because his ascension to Prime Minister wasn't completely without controversy, he definitely had to establish the legitimacy of his new government.

He starts right off by describing the War Cabinet he's appointed and how it represents all parties in Parliament. He asks for understanding about why this had to be done so quickly, and projects a generally confident and collaborative attitude. He knew he had to get everyone on board with the new government, and he lets the MPs know that he thought it was important to have this meeting right away so they could get up to speed on all the changes. He's not trying to establish his own credibility so much as the credibility of the new government he's formed.

So right off the bat he's showing the MPs some serious R-E-S-P-E-C-T, and what better way to have them take Churchill seriously.