C++ cross-platform version of Cocos2D, an open-source mobile 2D game framework.
Corona is a mobile development framework for creating high-performance, multimedia-rich applications, games, eBooks etc
"The consensus seems to be that corona is easier to use but that cocos2d-x has the advantages that come from being open source easy to customize merge with other code community etc"
from question "IPhone / iPad game application dev tools"
"I would recommend cocos2d-x as it is in my opinion equally or even better than corona and it is free"
from question "2d Mobile Gaming"