The funny thing with the avenger is that the censure has to trigger every turn or you are doing less damage then any other striker out there. If it triggers you are doing on par with the encounter powers and with your at wills you will be doing a little bit more compared to the Barbarian.
Compared to a ranger or rogue you will be doing about the same amount of damage with an at will if the the censure triggers. For all these cases I am assuming the avenger gets to use the oath.
Really it looks like the CoP Avenger is assumed to be triggering its censure about as often as a rogue is getting CA. Otherwise you will be doing substantially less damage.
Its not about damage, its about expected damage per round. Expected damage per round is based on both damage and accuracy.
If you do the math, Avenger damage per round with at wills is very similar to damage per round for other striker classes.
Here's a spreadsheet that calculations average damage per round for rangers and avengers given set in puts and assuming that the ranger uses twin strike while the avenger gets his oath bonus. I input starter values so that it would be more clear how the fields work. The starter values are a level 1 ranger with twin bastard swords, and a level 1 avenger with an executioner's axe, assuming that the ranger hits on a 9+, and the avenger on a 10+ (due to lower proficiency bonus).
The Avenger actually wins this lineup.
Heaven only knows how things change if you start messing with it and advancing the characters by level. Rangers double benefit from enhancement bonuses, but Avengers double benefit from accuracy bonuses. And Avengers have a lot of routes to improve things other than damage, like armor class, which aren't available to Rangers, so of course this sort of straight up damage comparison is only part of the story. Plus once in a while an Avenger DOES get that bonus damage that I've neglected.
You can add magical weapons to this chart, but for the record it assumes that whatever magical weapons the ranger has will have equal damage and critical values, and I don't feel like changing it to accomodate multiples because I'm bored now.
The document was originally created as a .odf, so I'm blaming any errors in it on the transcription to .xls for upload.