Mr Chauvel's comments came after Corrections deputy chief executive Christine Stevenson revealed Serco had vastly improved its performance at the 966-bed Mt Eden prison in 2012.
She said the British-based Serco had a "tough" first year in charge of the facility, failing nearly half of its targets. But it had turned itself around in its second year and was meeting 95 per cent of its targets.
Mr Chauvel said this claim was hard to evaluate without knowing the percentage of targets that taxpayer-funded prisons were passing.
Ms Stevenson confirmed the department was collecting performance measures for individual prisons and would publish report cards next year.
But she warned the information could present a misleading picture.
"It's quite a tricky thing to do. Our prisons ... are all a bit different. You have Rolleston Prison, which is low-security, doesn't have a fence, through to Auckland [Prison], which is maximum security."
Serco's $300 million contract at Mt Eden requires it to beat the public sector's results by 10 per cent, and if it fails to do so it is financially penalised. It has been fined $750,000 for errors so far.
The company was slammed for the high rate of serious assaults and escapes in its first 12 months, but it has been praised for its reduction in drug use rates.
Serco is expected to ensure fewer than 12 per cent of prisoners test positive, and its report card showed 3.88 per cent had been found with drugs in their system.
Taxpayer-funded prisons had a positive drug test rate of 7 per cent.
Serco has been given the contract for a new 960-bed prison in Wiri, to open in 2015.
Serco performance
Targets met at Mt Eden Correctional Facility
2011-12: 19 passed, 18 failed
2012-13 first quarter: 34 passed, 3 failed.
