I guess she's technically competent, but that's not the word I'd use to describe her in RE6. Unflappable to the point of complete unbelievability is how I'd describe her.
Leon is a competent character. A hero. So is Chris. So is Sherry. So is Jake, whom I also sort of hated. Every single one of them, at some point during the game, showed a bit of fear, confusion, self doubt, sadness, concern, or empathy.
In this game, Ada experienced: having her DNA stolen, being cloned, having said clone launch a genocidal attack on the entire world in her name, witnessing said attack first hand, being chased by a mutated version of an obsessive ex-employer, watched someone she supposedly cares about (Leon) being stalked, attacked, and framed for the murder of the president of the United States.
Seemingly enough to at least rattle even the most together person.
To all this, Ada reacts by issuing cheap puns, behaving in a completely level headed, shrewd, some might say borderline precognitive manner, mocking her clone, mocking the inhabitants of an infected city, mocking Leon for caring about her, swinging around skyscrapers in high heels, mocking military helicopters as they fired missiles in her direction, cracking wise about airliners plowing into urban centers, etc. etc.
Helena's sister showed more human emotion and relatable character traits in this game, and she was a hideous undead creature.
Further, while almost every other character in the game falls short in at least some portion of their campaign (Leon fails to save Helena's sister, Chris fails to save his partner, Sherry gets captured, Jake gets captured), Ada skates through the apocalypse, a government cover up, worldwide military pursuit AND all the worst parts of every other character's story with nary a scratch. Or hurt feeling. Or second thought. She never fails, she never falls short, she never seems to consider that she might. Luckily, should one of the other characters populating the story fail to live up to her level of perfection, she is constantly conveniently positioned to swoop in and bail them out, too. It's absolutely absurd.
If you're going to make a character so all powerful, at least make them likable. If you're going to make a character so unlikable, at least don't let them get their way every moment of a 50 hour game. The combo of Ada being both incredibly unlikable as a character AND completely infallible is a real drain.