I don't even know where to begin the responses. I kinda disagree with everyone here, to varying degrees. But I'll try to keep it short.
First, the idea that Cap represents the values of 1941 is false. That may be true for Ultimate Captain America, but 616/MCU Cap is everything America *should* stand for. He is the embodiment of the best values America has to offer even when they're not put into the best practice, despite coming from a time when racism, misogyny and propaganda were very common. There were plenty of ***holes in both 1941 and 2014. The First Avenger demonstrated that perfectly, especially with the grenade scene. Cap wouldn't agree with the prejudice going on today, nor would he be fine with the internment of Japanese Americans during WWII.
Second, regarding Cap's character arc in TWS...it's not about deciding between being a government stooge and thinking for himself. That's always been a part of his character, and he's been questioning SHIELD since the events of Avengers where his character arc was all about realizing there is still a need for his existence in the modern world. TWS takes that character arc and progresses it to the next level. It's about Cap learning where he belongs in the modern world, how to adapt to it without losing his core principles, and ultimately making the decision no one else could make (or were too hesitant to make). Several characters throughout the film tell him to give in to the new world and start anew, from Peggy to Fury to Pierce. "Sometimes to build a better world, you have to tear the old one down." That's what HYDRA believes and is their justification for their actions. He then takes that advice and spins it on its head by deciding to abolish SHIELD and HYDRA altogether, because they're two sides of the same coin. I'm sorry if you expected a more radical change in Cap's character, but Cap is more of a character who changes the world around him than himself. He has that in common with Batman. They both refuse to let anything change them as people or to compromise their worldview.
Which brings me to my third point...a character doesn't have to drastically change in order to be developed or three-dimensional, they just have to be given an opportunity for change. Whether or not they take that opportunity is what informs their character, and that's the basis of a character study. TWS is a great character study for Steve Rogers in that regard, because it's a fantastic love letter to everything the character embodies, what he really represents and how he refuses to let anything or anyone change him for the worse. If you ever thought Cap was a propaganda character, TWS is the film to prove you wrong. I believe that's what the Russo's set out to do.
Fourth, the idea that having HYDRA as the villains in TWS is a copout and takes away from the social commentary, because it's about *who* pushes the buttons as opposed to the buttons being pushed. I've heard that criticism before, and I don't think it a valid one. The message is that the world's become very grey-shaded, and the "good guys" here to protect and serve are in no way different from the stereotypical bad guys when you get deep down into it. It's why Steve decided both HYDRA and SHIELD needed to go down, because they were two sides of the same coin. Even the "good" agents like Fury have still been conditioned to adapt HYDRA's philosophy and point guns at the whole world. If anything, it's a rather controversial point to argue that a modern government institution can be the equivalent of the Nazi's.
Also, the KGB analogy doesn't really apply. They made it clear HYDRA infiltrated SHIELD right at its inception, and it's also commentary on how the Allies recruited former Nazi scientists after the war.
Fifth, the idea that Batman has no character arc in TDK...not true. The film is about him learning that Batman is who he is and there is no escape from it. "I've seen what I have to become to stop men like him", and in the end, he becomes that. The film is also a character study of what separates Batman from other vigilantes/the police/DA/ordinary citizens, as well as a study of the Batman/Joker dynamic. That's as far as I'll go into it, since this is the MCU thread.