Originally posted by Stoic
Not sure if you will answer this, but when you speak of mental fortitude, are you speaking of Batman's ability to remain calm, cool and collected? I need to point out that batman is far more eager to pop someone in the mouth when they get out of line than Captain America is. Steve never had the billions of dollars to lean on, which in and of itself means that he may have dealt with more hardships in total, and therefore has been tempered by this. How many times has Batman just hauled off, and punched out a team mate, compared to Captain America? Not killing the Joker is what makes him a hero. The same can be said of Captain America, Daredevil, and many other characters that will not willingly cross the line.
I'm speaking about how much a character can take mentally and emotionally before they snap or in the case of this thread, fall to corruption. In this case Batman has Captain America beaten by a land slide.
Having billions of dollars didn't stop Bruce from witnessing his parents get iced in front of him, it didn't stop Joker from crippling Barbara or killing Jason. The only noticeable hardship Cap had was his partner dying and it didn't affect him nearly as much as Jason's death did to Bruce.
The problem with your last sentence is that Cap has crossed the line, he was in WW2 ffs and by profession a killer. Yeah Cap isn't Punisher and will probably avoid killing his opponents if he could but isn't above doing so.
Meanwhile
Batman could of killed Alexander Luthor if he wanted to but didn't even though this guy was a threat to the universe and was directly responsible for the death of numerous heroes including Superboy.
I'm sure there is a theoretical point to where Batman will cross the line and kill someone but his threshold is magnitudes above Cap's.