When Kara puts on that suit, she doesn't take on a different personality than she has when she's not in it; all that putting the suit on does is give her permission to be a whole person rather than just 'half' of a person (which is what her life up until the point where she flies and rescues her sister and the other passengers on that plane had been centered on), whereas, with Clark, I've always felt he was one person as Superman and an entirely different person, one which didn't accurately reflect who he was, as Clark.
With Kara, she's Kara when she's got that cape on and she's still Kara when she's living her day-to-day life; she's just emphasizing different parts of herself.
Yeah the way Benoist has described it, when Kara puts on the suit it's pretty much just as empowering for her as it is for the actress. So I do think there's a part of that shy and awkward disguise of hers that is her true self. She probably just amps it up a bit more for the office.
So I don't buy the idea that's it's all just an act. And even in the costume she still has a lot of the same doubts and concerns at times.