Personally, though they're both great battles, I'm gonna have to go with The latter.

Both are well analysed IMO, and both have spectacular fight choreography. However, Bucky VS Jason has three things that make me prefer it.

First, I love Bucky using his arm to block Jason's bullets.

Second, I think the story is better- obviously, not all Death Battles need a compelling story behind them, but as opposed to Nightwing vs Daredevil, where it's just "I need that more than you, let's fight over it!" I like the little scene of Jason and Bruce talking, and the buildup to the fight as Jason realises someone's coming.

This kind of leads us to the third reason- I get that no-killing rules are turned off for Death Battle, but it's a little jarring to see Nightwing go from perfectly in character to remorselessly killing a man he just met while he's defenceless in the blink of an eye over a briefcase he could just walk over and grab while the sonic windings do their thing. Batman Beyond vs Spidey 2099 had this problem too. It doesn't ruin the fight or anything, and again, it's DEATH Battle, it's just a bit... I dunno.

Here, these two are both ready to kill. They carry guns for a reason. They aren't fighting over who gets to solve a case, either- Bucky's here for an elimination, Jason's not going down without a fight.

What do you think?