With the New 52, they totally did away with the whole Batman and Catwoman dynamic. In the old continuity, Catwoman knew about Batman's secret, and they were more heavily tied together. In Hush, Batman told Catwoman he loved her, albeit, Selena was in a coma at the time due to Hush having ripped her heart out. Though in the New 52, Catwoman and Batman had hot and heavy fight sex in the early issues of her series, and that was about it. Pretty much, the New 52 was retconning everything, changing character backstories, etc. Like, Superman and Lois Lane never getting together early on. The New 52 was supposed to bring all the universes into one, which included the titles from the sub-company, Wildstorm. About the only good thing about the reboot was teaming up Deathstroke and Zealot together.
Marvel at least tries to maintain some continuity, but that has floundered over the years. Marvel has done some things similar to what DC has done, but not to the extent of the "Let's ignore everything that came before". The last time Marvel tried to do a reboot was with the Heroes Reborn, where a bunch of heroes like the Fantastic Four, etc jumped through some portal and were living an altered life. Age of Apocalypse was the same, but it made more sense. Legion went back to kill Magneto, but instead killed Xavier when Xavier jumped in the way to save Magento. Magneto became a hero leading the X-Men, married to Rogue and with a child. Cyclops worked for Apocalypse same with Havoc. Gambit led his own outlaw group.
Chris Evan's portrayal of Johnny Storm, seemed in part similar to the early years of the character. Though he has done an excellent job playing Captain America. On a sidenote, apparently there was a rumor that when Man of Steel was being made, apparently they approached Erica Durance to reprise her role of Lois Lane, but she turned them down. She said it felt like cheating on her Smallville co-star.