Hmm. For someone supposed to be a master of The Game, Celene did not live up to the hype, in my opinion. Certainly, in one-on-one, small scale confrontations such as Gaspard vs Teagan, she does well. But bigger picture? Not so much. Which makes me wonder if she's really the Master people claim, or does she get the credit for particularly adept servants and allies? In most of their interactions, Briala seemed to be the one with a head on her shoulders.
The situation in Halamshiral, for example. What possible reason would there be for Celene to abandon the running of her nation to ride off and personally deal with a minor rebellion in the slums of one city? Does Orlais have no generals? Certainly she could have said "General la Fleur, take your troops and burn the Halamshiral Alienage to the ground", made a big public show of sending them off, and shown she was tough on rebels, elven or otherwise, without ever having to leave Val Royeaux. Problem solved.
Then there was her painful vacillation on the elven topic with Briala. "Oh, I'm totally going to improve the lot of your people, and make them cool, and, uh...well, I mean, maybe. Eventually definitely maybe. You know, right after I blatantly use them as disposable scouts with the Eluvian network...but then certainly maybe. If it's convenient. And the nobles don't mind. Hey, can we just pretend I didn't burn down an Alienage the other day?" She was so obviously not going to keep her promises that even the thickest characters figured it out. A real Master of The Game would have at least been able to lie convincingly.
Don't get me wrong. She's been Empress a long time, and that suggests she couldn't be completely inept. But was it a case of doing a lot of things right, or one of not doing too many things wrong? It did get to the point of her top nobles breaking into armed rebellion, after all.
When it comes to the Inquisition, though, her past (in)competence is of only minor concern. Neither contender to the Throne is incompetent enough that Orlais won't recover from the Breach, so stability will be restored. For me, it will be more about who can offer what I need to save the world, and who is most likely to actually follow through with their promises.