The Labour-led authority currently has five scrutiny committees, all chaired by members of the same party.
Opposition leader Andrew Eade said this "archaic” approach creates a "democratic deficit”, but Labour leader Shaun Davies pointed out that for some of the Conservatives’ last term in power, they did the same.
Cllr Davies said the committee chairs held the administration to account "without fear or favour” despite belonging to the ruling party.
They were speaking after Professor Steve Leach, who chaired an Independent Remuneration Panel that recommended an average 20 per cent increase in councillors’ allowances, said it is "healthy” to share scrutiny roles between parties.
Cllr Eade said: "I strongly agree with the comments of the review panel that this council’s approach is now unusual and not best practice.
"This authority needs to drag itself into the modern world and accept the value of having opposition members leading and chairing scrutiny.
"For three out of the four years between 2007 and 2011 we appointed a Labour member to head up scrutiny and we welcomed that challenge. I now accept that that, perhaps, wasn’t enough.
"Currently this council operates at a democratic deficit.”
He added that he saw the authority’s view of scrutiny as "somewhat archaic” and it should see the role as a "critical friend”.
Liberal Democrat leader Bill Tomlinson said: "I think the Conservative group took them away to start with, then the Labour administration carried on that practice, and I think it should go back to where it used to be where these chairs are shared out.
"From a public perspective, it doesn’t look so good when it’s the administration that appoints all those chairs. That doesn’t lead people to think the executive is being kept to account.”
Cllr Davies said the 36 Labour councillors, elected in May’s election, include some "very talented members”.
"The scrutiny chairs, without fear or favour, hold this administration to account,” he added.
"Members of opposition parties can hold this administration to account. Unlike some councils, we invite both the leader of the opposition and the minority leader to our cabinet. We are cross-party on a political weighting basis for every committee of our council.
"And, as Cllr Tomlinson quite rightly says, before 2007 we did operate a system, I’m told, where scrutiny chairs were cross-party, but that was replaced when Cllr Eade was the leader.”
Scrutiny committees are panels that examine council departments and can propose policy amendments.
Prof Leach’s recommendations, which included raising the special responsibility allowance for scrutiny committee chairs by just over £700 to £7,843, were approved by a majority of councillors.