I think that tying them together [economy and military] is absolutely necessary to understand the larger picture.
America has, as a nation, a very strong economy. An advanced army needs money, and lots of 'em.
If the US didn't have economic prosperity, it would not be able to maintain one of the worlds largest and most advanced armed forces. The US armed forces is in a special position, in the way that they're basically everywhere. Supplying and maintaining bases and outposts all over the world is expensive, but it also requires a very sophisticated infrastructure. This all requires money, and they would not be able to continually have the most advanced forces, if they don't maintain a large and robust economy.
To be clear, any superpower needs military power to stay in a position as a superpower. This can't be done without a large economy, so I'd say they're equally important, leaning towards economy.