Why yes, we did watch two Winnie-the-C movies within the span of a couple of weeks. Good catch. This one is much much better. Gary Oldman, playing Churchill, grabbed the Oscar for Best Actor. It also won for "Best Achievement in Makeup and Hairstyling" (because you probably couldn't tell that's Gary Oldman). And it was nominated for four more Oscars, including Best Picture.
This movie is set around the events of May 1940, roughly spanning the time between Churchill's becoming Prime Minister (May 10) and Dunkirk (starting May 26). In between is a lot of political skulduggery and uncertainty about the war. Churchill's own Conservative Party machinery doesn't like him much, but they're forced into making him PM due to pressure from Labor opposition. That doesn't stop people like Neville Chamberlin and Lord Halifax from advocating a negotiated capitulation to Hitler's "peace offers".
Churchill undergoes a crisis of self-doubt. Does he really want to preside over what might be a disastrous Nazi invasion of the sceptred isle?
Well, we know what happened. The movie makes things "more interesting" by having Winnie meet with a random sample of British citizens on the Underground to Westminster. This almost certainly never happened. Still, it was in keeping with Churchill's actual personality, as opposed to the previous movie's made-up cowardly persona.