I do, of course, realize that mostly everyone would pick Darth Vader. That's fine with me, because it's my opinion on the matter. Now, you mentioned acting, which I believe is entirely irrelevant because we're judging the characters themselves, not necessarily the performers. So, I would base my decision as if what happened in the movies was, in fact, actually happening. Even if you want to out of universally evaluate Hayden's performance, I would tell you that he won multiple awards for his performances in Attack of the Clones and Revenge of the Sith respectively.
I personally thought his acting was good in both films (especially where he wakes up in the middle of the night during RotS), despite his monotonous voice.
Yes. The majority would conclude that Darth Vader is more popular. I have no problem admitting that. Did you actually ever think of why he achieved such status? He was the main villain in a fantasy film that was advanced for his time (not to mention came out twenty some years ago). He was intimidating with his black armor clad appearance, and his voice. I myself probably would've thought he was "cool", too, if I were younger. But, I'm not particularly seeing how being a historical figure in the eyes of the public makes him a 'better character', nor would it change what I think.
And again, has the "majority" read any the Expanded Universe materials? Hell no. This has a lot to do with why I would choose Anakin Skywalker as he was in all his glory over Darth Vader, a shell of his former self. I merely like Anakin's attitude, his style (not lightsaber style; though, that kicks ass, too), his look -- the most important determining factor for me -- and like I said, I can sympathize with his character (not necessarily because I got scolded by my master, or got all my limbs strewn across lava banks, though).
And really, how a character appeals to me is very important. Darth Vader does not, therefore I don't really care too much about him. Anakin does, so he matters.
Now, yes, Anakin is "whiny", he's a "brat", but so was I, and I still am. Look at why he questions his master, and everyone else. He definitely was not meant to be a Jedi, yet he's on the Jedi path. I'm not going to justify his actions, or his words, because most times, he's rightfully reprimanded, but still. The point is: if you don't like characters that are annoying to you, that's great for you, because different people have different interests that they look for.
I apologize (not really) that I find characters who I do not think have any sense of interesting personality [in the movies] inferior to those who do.