In an immediate test of how they fared, a show of hands among the audience of Conservative members saw more people plump for Mrs Badenoch than Mr Jenrick.
However, Mr Farage appeared to dominate both contenders' pitches to the Tory faithful.
Mr Jenrick insisted he has the Brexit champion "rattled" and added: "I want to retire him." The former immigration minister said the only way the Tories could return to power was by winning back Reform voters or those who opted to stay at home in July's election.
Meanwhile, Mrs Badenoch said, as an "engineer", she could fix the UK's "broken system", and that her plainspeaking matches the Clacton MP's.
Engineer
Mr Jenrick blamed immigration for the Tories' defeat at the polls, adding: "It's the reason we lost four million of our people to Reform and millions more who decided to stay at home.
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