The evidence is expert opinion on false confessions and a recent assessment that Pora is affected by foetal alcohol spectrum disorder.
The other ground of his appeal is that because of an error by his lawyer, the significance of Malcolm Rewa's erectile dysfunction was never put to a jury.
Rewa was convicted of rape but two juries could not decide whether he was guilty of murder after semen from Ms Burdett's body was found to be his.
The Crown will be represented by Solicitor-General Michael Heron, QC, Dr Mathew Downs and Zoe Hamill.
His case is likely to be the last New Zealand sends to the Privy Council, following establishment of our Supreme Court in 2004.
Judges' task
The judicial committee of the UK Privy Council is examining:
• Whether the NZ Court of Appeal was wrong to uphold a ruling that restricted evidence relating to the modus operandi of the appellant's purported co-offender, Malcolm Rewa.
• Whether the committee should admit and consider fresh evidence raised by the appellant.
• Whether a substantial miscarriage of justice was caused by the failure of the appellant's counsel to raise material points.
• The panel is: Lord Kerr (chair), Dame Sian Elias, Lord Reed, Lord Hughes, Lord Toulson