Some differences between The Moose And The Sparrow and On The Bridge are their endings. In On The Bridge the story ends happily. Seth realizes how Adam isn't actually cool and that he doesn't need cigarettes and jackets to be cool. While in The Moose And The Sparrow the ending is more tragic and has a bit of a cliffhanger.
Differences
On The Bridge
The Moose And The Sparrow
Cecil take this to go get sharpened
In both the short stories the protagonist is bullied by a bigger guy and is able to do nothing about it but say no. In The Moose And The Sparrow Cecil is bullied by Maddon and all he could do was take it. In On The Bridge Seth was bullied by the people in the car and all he could do was not lick it.