By default Vivienne is more powerfull, as KE she owns everything... Soloing dragons, soloing fade demons, she could've saved the world.. (Same could be said for the Inquisitor if s/he is a mage and KE however). And yes you can deny Vivienne from joining and no she can't close rifts...
I don't know, all of them have their good and bad sides.
The Warden is the most 'iconic'? of them all, s/he came from 'nothing' and build an army, survived Ostagar (with some help so did Hawke) stopped a civil war, discovered the Urn, saved Redcliffe, helped Orzammar, saved the elves/werewolves (depending on choices made) Killed 2 dragons of 1 an Archdemon, Saved Amaranthine/Warden base and could even become King/Queen (Prince Consort?). Also killed the blob and Architect (or not)..
Well Hawke... Same goes for the warden, wouldn't be alive if Flemeth didn't save him/her. Ended up with 'none choices' no matter what Hawke did nothing changed regarding the outcome. Maybe if Hawke wasn't there the Qunari would still have Kirkwall or the templars/mages would've taken it back somehow? The rebellion would've happened anyway, and thanks to Hawke Corypheus woke up and Red Lyrium got introduced to the world... (Even if you didn't have the DLC)
The Inquisitor.... Got the anchor because... 'luck'? Wouldn't know what to do with it if Solas wasn't there i guess, survived the attack on Haven because 'luck'? Managed to do most things because the Inquisition was there, didn't do much alone. Attacked warden fortress with force. True if you side with the mages it shows the world is gone, demons roaming allover but it doesn't quite say Corypheus became a god? (Not sure here). To me the inquisitor felt more like a tool, the only 1 able to close rifts. The inquisition could've just dragged 'him/her' around in a cage and pointed his/her hand at the rifts.
What i wonder is, how does it go in the books themselves? What happens there? I've read none of them, i did read some of the comics? But they were mostly about Varric and Isabella trying to save Marric and meeting Sten again. Don't think that matters really.
Also some comic about some mage girl who was the daughter of a templar and a mage.
And seen that movie with Cassandra becoming the Hero of Orlais.
Overall to me the Warden is the most powerfull/iconic of the 3, it felt more 'me against the world' and it had more story to it and background. Hawke did goto Kirkwall to be safe from the Blight trying to save the family, at which s/he fails miserably.. If you play your cards right only Gamlen is alive in the end..
The 'Inquisitor' was/is a tool, bringing flowers to places, filling requisitions, took a lot of strolls, worried about curtains and what the windows should look like and what throne to sit on and what bed to sleep in and don't forget the courtyard/garden/tower. Went to a party in the Winter Palace where s/he danced a bit and talked/listened to people while sneaking off to plunder the palace.
To me Warden->Hawke->Inquisitor.
And i don't look at the games themselves because that would be DAO->DAI->DA2.
And what i'd like to see is DAO done in the FB3 engine
(You can dream right?)