For one thing, both logos incorporate a wing element. So that's interesting. While the Red Wings logo has been around forever, the Blues is a little sleeker. I would almost venture to say that the same guy who designed the Flyers logo had a hand in the Blues. As far as aesthetics, the Blues logo has the edge.
This will be complicated. The situation here is that both teams have a color as part of their names. To determine which is superior — red or blue — we must look to the American Revolutionary War. Since the British fell, the Red Wings are obviously inferior to the Blues. (I warned you to expect some crazy nonsense.)
As I mentioned, both logos have elements attached to a wing. In the Red Wings case, it is the primary element, the wheel being there to represent the Motor City of Detroit. In the case of the Blues, the musical note is the primary element. The attached wing — I'm not really sure about why it's there.