Beautiful Dirty Rich - I love Gaga's live version of Bang Bang but the album version is soulless and deserves its status as a bonus track. All the Cheek to Cheek songs sound so much better live than they do on the album, they clearly couldn't capture that magic in the studio unfortunately.
Can't compare them because they're so completely different. It's like choosing favourite child lol. I love both equally for different reasons. Beautiful Dirty Rich is from back where my love for Gaga began, and Bang Bang is what my love has grown into <3