Where does a wounded political party start after suffering its worst defeat in a general election ever?

It is a big question, and both Kemi Badenoch and Robert Jenrick have a different prescription.

The two remaining candidates in Conservative leadership race – after centrist James Cleverly was ejected by MPs – are both young and seen as being on the right of the party.

But there are plenty of points of difference for Tory members – who begin voting soon – to chew over.

Badenoch, the 44-year-old former business secretary, has argued for returning to core Conservative values.

“You start with principles first, not throwing out a succession of policies,” one Badenoch campaign source said.

The actual plan for renewal, Team Badenoch says, will come in time. Her campaign is entitled Renewal 2030 – which she says will be her first year as Conservative prime minister.

A source from Jenrick’s team said party members faced a choice between a candidate with detailed policies to fix the NHS, the economy and migration, or “risking being drawn into endless” spats and distractions.

In his conference speech, 42-year-old Jenrick laid out five key changes for the party to challenge Labour: an immigration cap, opposing Labour’s “mad plans” on net zero, embracing housebuilding, reducing the size of the state and “defending our culture”.

Badenoch is known for her direct approach and willingness to speak her mind.

At the Conservative Party conference, there was controversy over her suggestion that maternity pay had “gone too far”. She later said she had been “misrepresented”, but the criticism drowned out her campaign.

But Badenoch’s pugnacious approach to debate means she “has cut through to the public,” says supporter and conservative commentator Albie Amankona.

People see she is “fiery, opinionated, brave and competent,” without the need to be attention grabbing, he adds.

Her allies see hints of Margaret Thatcher in her take-no-prisoners style. Jenrick is also a Thatcher fan – one of his daughters has Thatcher for a middle name – but Badenoch’s supporters have accused him of being a “shapeshifter”.

Seen initially as an ally of David Cameron on the more “moderate” wing of the party when he became an MP in 2014, Jenrick has shifted to the right after quitting as immigration minster last year.

Those backing Jenrick insist his right-wing credentials are bona fide.

Jamie Mulhall, a Conservative councillor in Derby, called Jenrick a “conviction politician” whose views adapt when evidence changes.

Mulhall, who is part of Jenrick’s campaign team, said the former minister likes to “step back and has had a good long hard look at what happened” before coming up with the “clarity, vision and polices that appeal to the common-sense common-ground”.

Cutting immigration is a top priority for both candidates.

Robert Jenrick’s signature policy is UK withdrawal from the European Convention of Human Rights (ECHR), which he argues had made it “impossible to secure our borders”.

He describes the idea of reforming the treaty – as some Tories want – as a “fantasy” and has said all members of his shadow cabinet will have to share his position on this issue.

Badenoch has said she would be willing to leave ECHR if necessary but thinks wider – and deeper – reform of the British state and the immigration system should be tried first.

Focusing on the ECHR “shuts down the conversation we need to have with the entire country” about migration, she has said.

Sometimes labelled a “culture warrior” – a tag she disputes – Badenoch is popular with many on the right of the party for her “anti-woke” stance.

As equalities minster, she gained attention by rejecting claims of widespread institutional racism in the UK and fighting to preserve single-sex spaces for women over gender-neutral toilets.

At the party conference, Badenoch told the Sunday with Laura Kuenssberg show “not all cultures are equally valid” when it comes to deciding who should be allowed into the UK.

Jenrick has in the past stayed away from these hot-button topics, reportedly warning young activists in his party not to “go down a rabbit hole of culture wars”.

But in his conference speech, he vowed to “take a stand to protect our nation, culture, identity and way of life” which he said were at risk due to mass migration and a lack of integration.

Both candidates have served in the cabinet, but their journey there could not have been more different.

Born in south London, to parents of Nigerian origin, Badenoch grew up in the US and Nigeria, where her psychology professor mother had lecturing jobs.

Her exposure to instability in Nigeria “a place where fear was everywhere” forged her conservative appreciation for “security, democracy, equality under the law and above all else freedom,” Badenoch said.

She is married to Hamish Badenoch, a banker and former Conservative councillor – they have two daughters and a son.

At the Tory conference in Birmingham, Jenrick described himself as “a Midlands man” – having been raised in Shropshire while attending a private school, Wolverhampton Grammar.

After working as a corporate lawyer in London and Moscow, he moved into business, becoming an international managing director at auction house Christie’s before becoming an MP at the age of 32.

He is married to US corporate lawyer Michal Berkner, the grandchild of Holocaust survivors. They have three daughters.