Hm, lots of people seem to be speculating a lot of this through gameplay elements so I don't know how anyone wins that really, we're all going to have it different there. My warden didn't even touch the archdemon, Alistair soloed him (and most other big bosses) with warden either dead or throwing heals out. As far as my game is concerned, Warden was a nobody and didn't really do much besides gather treaties, but of course the story sees him as this huge hero. He was also not the same warden who killed Mother for me and Architecht was spared. So...
Alone, neither Warden nor Inquisitor have actual solo achievements as far as the story goes, unless your Warden died fighting the archdemon. ie. landed the killing blow and accomplished that by themselves, although Riordan weakened it and it's generally assumed that the party and armies helped also, but the sacrifice is optional. If he survived killing it, it is because Morrigan saved him.
Inquisitor had the same deal with Corypheus. Morrigan/Dragon + inquisition forces weaken Corypheus, leaving him open for Inquisitor to finish him off. This is canon in every playthrough, Inquisitor always gets the killing blow. Earlier in the game, an inexperienced Inquisitor can not stand up to Corypheus and the fake archdemon alone. An experienced Inquisitor can use the Rift to do some really powerful stuff, this is canon, regardless of how strong you want to headcanon your warden and hawke. He takes this above swordfights and magic in to something larger and more primal. Who is the better mage, fist fighter, sword fighter of the three? Who knows. Evidence would point to...
Hawke has one solo accomplishment of defeating Arishok in combat, which the CG trailer show to be far more interesting than how the actual video game system presents it. Hawke fought a weakened Corypheus with a small party and defeated him without any armies or rifts, but did not kill him. Inquisitor had knowledge, tools and time, Hawke didn't. He also took down a rampaging horde of qunari with a small group of friends but Meredith is generally given as a community effort from a larger group of people.
So i would say, Hawke is the guy who is gonna win a fair fight (because he has, single handedly, against an experienced and battle trained Qunari leader.) but he's not gonna do much against a rift or an archdemon besides slow it down. The arishok fight is also optional, if he isn't killed, the best thing Hawke did was stop the qunari hoard and the rest was mostly political. He has an option to possibly be dead. If he walks away from that nightmare demon and returns to us in the future, he is one BAMF. :/ A lot of his story is told to us by Varric so he could be weaker, he could be stronger. We don't know.
Warden's the guy you'll want to call for a Ferelden crisis because he is a figurehead, but beyond that he's only as strong as you wish him to be, since his non political accomplishments are all way too optional. If he did everything himself he's a powerful hero but theres too many variables and a chance that he can walk out doing barely anything beyond being a figurehead. Plus he can be 100% confirmed dead and no competition. I can headcanon him as the fastest, strongest, smartest, most powerful human in the world but it doesn't really mean much to anyone but me.
Inquisitor has access to a kind of raw power that pretty much trumps anything it's come up against. His magical and physical strength, like wardens, is going to be up to your ability to uplay or downplay it. A lot of Inquisitors fame, again, is political but he is renown for being part of an efficient strike team that always achieves victory and never loses men. He has the option to drink from the well giving him access to a great deal of knowledge. He is dominating both the battlefield and the political world and so far there is no way to kill him off. =I
So toooo many variables to say who is what here but Inquisitor is looking to be in a different league. I say screw it all and lets have all 3 on the same side. What a team.