Councillors opposed to increasing mayoral powers also argued that the bill was poorly worded, too vague and could lead to problems.
But deputy mayor Gordon Chesterman said councillors had blown the additional powers out ofproportion.
"I think the concerns around this super-duper mayor are exaggerated and it's still fundamentally one vote on most things."
Mayor Julie Hardaker rejected suggestions of a move towards autocracy, and said having an executive mayor would be good for democracy and would ensure there were more "enhanced checks and balances" at a higher level.
She assured councillors there were no attempts to withhold information from councillors or from the public.
The committee also voted to leave unchanged the definition of the purpose of the local government, which involves four "well-beings" - economic, social, cultural and environmental.
In its submission to the local government and environment select committee, the council also criticised the quality of policy analysis and raised concerns about the bill not being evidence-based.
The council has been working on its submission since last month, and the council voted unanimously on the final document.
MORE POWER
For
Julie Hardaker, Roger Hennebry, Gordon Chesterman, Maria Westphal
Against
Angela O'Leary, Ewan Wilson, Pippa Mahood, Martin Gallagher, Dave Macpherson, Daphne Bell, John Gower, Peter Bos