Right off, both logos have a lot of complexities though we find a lot more in the Capitals, obviously. On the other hand, its colors are appealing and used well. The Penguins makes use of only a single color outside of black and white (albeit a good color). Despite the Capitals' use of a script spelling out the team name (and city) within in the logo, it still squeaks by with the point.
If we assume the Capitals are lawmakers of some sort, then it's their job to write laws to protect Penguins and other animals. They therefore have the upper hand.
Washington, D.C. is the capital of the United States so the name seems like a rather obvious choice. But as far as the name goes, my question is: What is a Capital? A Penguin is a little ineffectual flightless bird. Regardless, I don't know what relevance Penguins have to the city of Pittsburgh as Penguins tend to live in rather chilly locales.