Cooley mentored the attack of Andrew Flintoff, Steve Harmison, Simon Jones and Matthew Hoggard that last year helped England claim its first Ashes victory in 18 years but returned to his homeland last year to work with the Australian bowlers.
Asked who he thought had the stronger attack, Cooley told Australian Associated Press: "I think we have."
Cooley trained England's quicks in the art of reverse swing to devastating effect in the last Ashes series and said he was now teaching the Australians the same skills.
"You want to try and have all the deliveries underneath your belt. Reverse swing is one of them, and if the conditions suit, you really want the bowler to be able to use that ball.
"We'll be trying those sort of things. If conditions suit, we'll definitely try to take advantage of it."
But Cooley said England would still have a strong attack, even if injury keeps leading reverse-swing exponent Jones from making the tour.
"They have a very good, formidable attack, and on our day when they're all firing, it'll be a good shootout," he said.
"I'm sure they'll be getting themselves organised. They're very good at looking after themselves, and it will be good to see them over here firing, ready to go."