Why not both?

In an interview, you need to impress, and that's true for both the job-seeker and the hiring team. So yeah, you need to talk a bit about your accomplishments, and it's hard to do that without being a little braggy. But you can let your work be measured on its own. If you directly measure your accomplishments against the other person's, and especially if you put their accomplishments down, you're not selling them. You're showing off your personality flaws, even if you "win" the pissing contest.