Winter Soldier debuted a month earlier, but Red Hood unmasked (un-hooded?) himself first. Another coincidence: both writers claimed they'd had this idea since they were kids. Captain America writer Ed Brubaker had wanted to bring back Bucky since he found out the character's death was a filthy retcon at age 9, while Batman's Judd Winick said he was one of the 5,271 fans who phoned DC to try to save Jason Todd's life in '88. Winick later admitted he made up that story for an interview, but it's possible he was just fed up with internet commenters accusing him of writing fan service for his own teenage self.
After Batman and Cap's "deaths" in 2007/2008, both disgraced sidekicks tried to fill their mentor's tights, but with a twist: 100% more guns. Bucky became the new Captain America but Jason didn't last long in the Batman role, being a dangerous nutjob and all.