To the OP, a worthy thread, as I think comparisons were inevitable, so big ups to you.
Okay, for me it isn't even close. Bale by miles.
But, let me also say that Evans has really come into the role as Cap.
I found him dull in both CA, and The Avengers, but this time he was a little
more comfortable with the role, and did a very good job. I actually liked his
Cap, and I HATE Captain America, so for Evans to get me on board,
well done him.
Okay, here's why IMO Bale's better.
1) He's playing 3 characters. Batman, Bruce Wayne the public face, and the real Bruce Wayne - this was very clearly established in Batman Begins, and Bale ran with it in TDK.
The three are different, but believable. The reason being is that Bale is a truly great actor, Evans is becoming a good one, but he's not in the same league. ( If you don't believe me, go see the Fighter ).
Let's face it Evans as Cap is just playing one character, so advantage Bale.
2) Bale's inner conflicts as the different characters are much more nuanced, compared to Cap's. For Cap its just whether he needs to be a good soldier and follow orders, or fight for the freedom he's supposed to represent.
Evans did a good job with Cap having to make that decision, but Bale had to really plumb Batman's most inner reserves and question the legitimacy of the character itself.
the next two are more about the whole film, and why Bale was able to outshine Evans, other than superior acting ability.
3) This is not a reflection on Evans, but Bale had better writing to work with, in terms of the character. I thought CA TWS was well written in general (which again is saying a lot as I loathe the character), but Nolan and Goyer made us really go on a journey with Bruce Wayne.
4) Bale had a better supporting cast. Jackson and Redford were very solid, Johansen was okay and Mackie was good. But none of them hold a candle to Oldman, Caine, Freeman, Eckhart and of course, Ledger.
I suppose you could argue that this might makes Evans better, as he had less to work with (in terms of supporting cast), but I think through his interactions with these amazing actors Bale really showed off what he could do (particularly in his scenes with Caine and Oldman).
I do give the edge to Evans in terms of the choreography of Cap's fighting style - a lot flashier than Batman's but a better reflection of what he's like in the comics, and very impressive on the screen. It was so well done that it looked like he actually could beat up GSP ( of course in real life Evans wouldn't last more than 2 seconds against Georges), but that just shows how good the choreography was.
I liked Batman's fighting style being heavy handed, but I think it was best portrayed in Batman Begins. (mind you it would be very hard to pull off any kind of high kick or acrobatics under that suit).
So Bale all the way, but well done Evans for a huge improvement and an enjoyable performance as Cap.