Ducati's has not won a race since the 2014 Australian GP but last week in the fine pre-test I Qatar they topped the testing times with Dovizioso and team-mate Andrea Iannone.
The MotoGP season kicks off on March 29 at Qatar's Losail circuit.
In a chat with Italian newspaper Gazzetta dello Sport, Dovizioso said he felt that they were stronger and more competitive than in Stoner’s day.
"I believe nowadays we are stronger and more competitive.
"Back then Casey would dominate, but it was mostly down to himself making the difference, as in fact the second Ducati was nowhere near. That means the bike wasn't so competitive.
"Now, instead, the GP15 is competitive, it's basically normal and it works. Now it's up to us to work on the details to make the difference and win."
Dovizioso feels that a podium would be a bonus at Qatar’s Losail circuit as he expects the factory Hondas and Yamahas to be stronger than they were in the Qatar test.
"We go to Qatar to get on the podium," he said.
"We were quick in the tests, but I know those four rivals very well, I know the bikes they have, how they work in the tests and on race weekends.
"To get on the podium will be very difficult anyway," he added.