The move may appear hollow given that the All Blacks, the number one-rated team in world rugby, currently hold both the Bledisloe and Tri-Nations trophies.
But Henry echoed Ireland skipper O'Driscoll, who voiced his preference for the Australians after his Triple Crown winners fell to back-to-back defeats against the Wallabies on their recent Oceania tour.
Henry, whose side host John Connolly's men in Christchurch on July 8, said: "I think we're a bit behind Australia at the moment.
"It's a big week for us next week. It's going to be a huge Test match at Jade Stadium. It's going to be a boomer.
"He (Connolly) has picked a bigger pack and bigger loose forwards, so they have a big lineout.
"They have four genuine targets and he's looking to right the scrum. They did pretty well against Ireland."
Henry has recalled Reuben Thorne for the Tri-Nations tournament, also including South Africa.
But several players named for the Irish and Argentinian trips - including Jerome Kaino, Craig Newby Casey Laulala, Sam Tuitupou, David Hill, Clarke Dermody and Mose Tuiali'i - have been omitted.
Troy Flavell, Nick Evans, Sione Lauaki, Angus Macdonald, James Ryan, Sitiveni Sivivatu and Conrad Smith were not considered through injury.
Henry also included Auckland hooker Derren Witcombe on that list following his return to club rugby after a serious neck injury last year.
Witcombe may take part in Auckland's Air New Zealand Cup bid next month as cover for Keven Mealamu.
The All Blacks squad have a meeting together in Wellington on Thursday before assembling on Sunday in Christchurch for their build-up to the first Tri-Nations test against Australia on July 8.