Killing off Captain America in the comics made national news. National news!!
Killing off Batman/Bruce Wayne made some 3rd grade news in online news sites under the entertainment section.
Need i say more? Apart from Superman and Batman it seems DC has nothing more concerning public interest.. i always hear so much about Wonder Woman and how she is the third character in the DC "Big Three" but to be honest.. the public knows next to nothing about her and most movie fans are too young to even remember the show with Lynda Carter from the 70s (are there even current reruns somewhere?).
Public also means mainstream people who don't watch the animated shows and movies where she features prominently.
However ask some random person and they will tell you about half a dozen Marvel characters even if they may not go that deep into it other than "that bald guy in the wheelchair" or Wolverine. Marvel has simply won the popularity race against DC.. if there ever was a race that is.
Part of it is simply blind luck though in my opinion.. what would have happened if Singer made a DC team movie and started the superhero movie genre again? Marvel got lucky.. Blade was a modest hit though most people didn't know (or still don't know) that he's a Marvel character. X-Men ignited the whole genre again and only then did Marvel make the right (and bold) choice to go all in with Iron Man.
They got lucky with Robert Downey Jr. because let's face it.. IM is a pretty generic story about someone having a change of heart and becoming a hero (and in this case some visual effects eye candy on top) but Downey really sold the role and made the movie a hit which started the whole snowball to avalanche system thus far culminating in The Avengers.
DC is hopelessly lost.. everything they do will either be lauded as copying Marvel or just downright silly or uninteresting. They need that one spark.. either a breakout movie or someone who understands and loves the medium like Singer or Whedon to take the reigns and create something that people will want to see.