Why? If you're asking why to my first statement, then because Bullseye got some pretty solid hits in before Frank got the upper hand on him.
For the second statement, it's because Crossbones is practically a super-soldier who can hang with and has beaten a good healthy Captain America. Punisher has admitted before that in hand to hand he would lose to Cap, so I reckon he would lose to Crossbones without weapons or prep.