It's funny. I never noticed the similarities between these two logos until just now. Both have wing-like elements on the left side and semi-circles on the right. Anyway, the Flyers logo has the same problem as the Sharks in the West. Too much black and not enough of the primary color. Find a way to make this logo more orange and then we'll talk. Until then, despite being a little heavy-handed with the detailing, the Senators logo is so much cooler looking.
Within the government, the Senator holds a lot of power over what laws should be passed to, say, protect endangered species, some of which may Fly. I know, a stretch, but you come up with something better. Seriously, comment away if you feel like it.
I'm not entirely sure what a Flyer is meant to be — perhaps a generic bird of some sort — but this competition is about logos, not team names. And when you say Philadelphia Flyers it's difficult for me to picture anything but the winged "P." So I'd say they got it right. I'm just not as happy with the Senators logo. I've heard rumblings that the Sens will go full-time with what is currently the third jersey logo. It's light years ahead of this one and I'd love to see them do it. Maybe then they can have this particular point.