I am myself doing CA for last 5 years and currently work in EY as a trainee. as per my analysis, the level of earnings is higher for CAs at initial phases but MBAs of good universities outperform CAs in advanced levels.
CA is just about learning each and every technical aspect of accounting, auditing and law. They may have technical knowledge more than any other qualification possessor. CAs are sometimes referred to as Accounting watchdogs.
The area where MBAs/BBAs outperform CAs is personality development traits and presentation etc. In universities, students continuously prepare and give presentations, hold and attend conferences, manage/organise different events etc and most importantly indulge in all extra curricular activities. CAs just learn/memorize books in their homes/ colleges and at the end give written exams, thats it. This system of CA education diminishes other skills of students (i am referring to Pakistani CA education). Colleges offering CA education here are established in plazas, homes etc.
This phase of the students' life is where their learning curve is very steep and the student develop skills which CAs lack. That is why most of the CEOs of the companies are MBAs.
Else, the level of earnings also depend on other factors like luck, references etc. Recently a friend of mine who is an ACCA with 2 years articleship experience got job in a reputable power company with 150k plus salary, because he had excellent communication and presentation skills. He is chosen over fully qualified CAs who also appeared for the interview.