Where I work? Chief Engineer for either one of the in-design/development programmes or on an exiting platform (air, naval, lad etc) is the pinnacle engineering job with safety, engineering, regulatory and financial responsibilities for their platform in addition to political and diplomatic skills to bring industry, operator and owner parties together. If it's air or nuclear then you have additional responsibilities as well.
Any higher up the chain, you aren't really an engineer anymore. More an administrator.