In my experience the people who think CA2 gave her Sharon’s personality/role are Sharon Carter fans, not so much diehard comics Natasha fanatics.
As someone who likes Sharon Carter I do think the MCU has done her wrong and kind of boiled her down to only the love interest aspect of the character, rather than the compelling foil to Steve that she can be when used well. Sharon in the comics was be pretty conflicted about abandoning her duty and job to follow Steve in Civil War, and removing that internal conflict gives her a lot less to really do in the movies.
As to whether Natasha has Sharon’s role, well, that’s something else. If you see Sharon’s role as “being a spy” and “being cynical foil for Steve”, then yeah, that is what Natasha does in Captain America 2. But a lot of characters share those traits in Captain America stories, including, like, Wolverine and Nick Fury. Natasha has served that role from time to time, too, notably in the Ellis Secret Avengers comics that featured Steve in an uncomfortable role with SHIELD. Those qualities are both pretty broad and entirely in keeping with Natasha’s personality.
But I see Sharon’s specific role in the Captain America mythos as more detailed than that. Sharon someone who grew up believing in the sort of values that Steve sells by breathing, who joined SHIELD to honor Peggy Carter’s legacy. Sharon is driven by a dedication to duty and service that mirrors Steve’s own, and that inspires and undermines their romance. Predictably, she and Peggy both suffer for being women introduced in the Silver Age, and Sharon dies and becomes one of the many people Steve feels he has failed. But then Sharon comes back, traumatized by years as a deep cover operative, and feeling betrayed by Steve for never rescuing her, and betrayed by the things he represents for the hell she went through subsequently.
The Sharon of this era probably occupies the place Natasha has in Captain America 2 the most directly. Natasha and Sharon both have a semi-flirtatious rapport with Steve and have more brutal methods. They challenge his idealistic way of thinking over the course of the story, but at the same time are drawn to his dedication to doing the right thing.
But importantly, for me, Sharon’s relationship with Steve is colored by her own past with Steve and by Steve’s own perceived failures. Natasha in CA:TWS, on the other hand, is more informed by her own attempts to find redemption and her complicated relationship with trust. Steve’s skepticism of Natasha is motivated by her own past betrayals and reputation, something that mirrors her early experiences with the Avengers and SHIELD in the 1960s, and her decision to leave SHIELD and spying and look for herself elsewhere is frequently repeated in Black Widow stories.
Also, the role that Sharon plays in Brubaker’s Captain America run isn’t that, cynical, flirtatious deep cover operative; her role in that story is one of Steve’s tragic true love. That plotline goes places the films never do, with Sharon being brainwashed and pregnant and in love, fighting off her attackers alone. In some ways, with Bucky’s reintroduction as the Winter Soldier, he’s the one who comes to occupy the narrative space that Sharon did in the Mark Waid run, and Sharon’s later brainwashing is a mirror of Bucky’s trauma.
What I’m trying to demonstrate here is that Sharon Carter is both pretty cool and constantly screwed over, but also that comics don’t always repeat themselves but often rhyme. And so a lot of similar stories get told with the parts rotating around, creating a thematic continuity. And that’s kind of what adaptations hold to.
I was initially pretty skeptical of Natasha having a larger role in Captain America 2 because I was worried, as always, that it would be handled poorly, and because I was especially worried about them handling Bucky/Natasha, a pairing I like, in a way that I didn’t. I was generally pretty pleased with the film though, and most of the story beats it hit felt true to Natasha even if the details were mixed around.
For me, Natasha’s appearance in Iron Man 2 was mostly unremarkable and bland, which was still a step up for movie superheroines, so I was mostly glad they hadn’t totally screwed her up. I really liked Avengers, and from there I just kind of pick and chose the parts of each film I like instead of taking them as separate incarnations. One criticism I do have of Natasha’s role in Captain America 2 that I haven’t seen echoed elsewhere is that by sticking these beats into a Captain America story (instead of the Avengers context where they happened originally, or even better in a standalone BW film) they sort of end with Natasha’s moral journey framed in terms of the triumph of Steve’s idealism.
I’d say that “Steve is always right” is at least accurate to the comics, but one of my favorite things about the original Winter Soldier comic is how Steve wasn’t successful in getting through Bucky’s brainwashing, and needs to use the Cosmic Cube to do it. So maybe that’s where my real dissatisfaction comes from. Who knows?
I also find there’s this impulse to criticize MCU Natasha for “taking over” things that rightfully belong to other characters— Wasp’s place as a founding Avenger, Bobbi’s batons and her relationship with Clint, Sharon’s role in Winter Soldier— just as there’s an impulse to blame Carol for getting the solo film that Natasha hasn’t. I don’t think that’s a particularly great way to frame feminist media criticism or a particularly fun way to be a fan, but that’s another convo entirely.