Among current ACC members, Duke ranks 4th in ACC conference championships, with 7 since the conference formed in 1953. Most recent was 1989.
In addition to those 7 conference championships, Duke was Coastal division champion in 2013 and played in the championship game (losing to FSU, which went on to win the BCS national championship that year). The ACC football championship game began in 2005.
In addition to Duke, speaking of "like minded, similarly situated" institutions:
- Wake Forest has two ACC championships (most recently in 2006), and was its divisional champ just last year.
George Tech (who I view as similarly situated) has 2 ACC championships since it joined the conference in 1983, mostly recently in 1998. In addition, it has played in the championship 4 times (in 2006, 2009, 2012 and 2014). And for the record, Tech had 5 SEC championships.
UVa (who I view as similarly situated) has 2 ACC championships and also played in the 2019 championship game.
Also, in this century, VU has been to 6 bowls. Duke has been to 6, UVa 10, Wake 11 and Georgia Tech 17. In this century.
Bottom line: while Clemson, FSU and Va Tech have dominated ACC championships in recent years, the ACC schools most like Vanderbilt have been much more competitive within their conference than VU has been in its conference. Which has also allowed them to go to more bowls.