There are distinct differences, even just from the statements regarding them on the EC Council and ISACA websites.
To answer your headline question: where does C|CISO stand:
At the moment, nowhere, but they are aiming for a slightly higher grade than CISM. I'm not sure how well it will work though; CISM is for experienced security management and not pretending to be anything higher; C|CISO is aiming at CISO's and those planning to be CISO's soon but appears to have remarkably similar entrance criteria to the CISM.
It is an interesting change of direction for the EC Council - the C|EH is at the opposite end of the spectrum: a beginner's security testing cert - so I will be watching to see how it goes. I have asked them for more information and will be sure to discuss further once I know more.
(disclaimer - I am the President of ISACA Scotland, but not biased - I am also the Chairman of the Scottish branch of the IISP, and believe in the value of certs where appropriate)
Update - I grandfathered in to the C|CISO at the end of 2012, and it looks like my original assumption is correct. It is aimed at the wider CISO experience, not just a security manager, but brings in elements that a CISM doesn't necessarily need around wider business risk, board level decisions and strategy, and a more holistic business view.