Rooney went on to have the more successful career overall of the two forwards, but Owen - in a debate prompted in a recent interview with Rio Ferdinand - feels his achievements in their initial years were greater.
Owen, who won the Ballon d'Or when he was 22, wrote on X: "At 17 I scored 18 PL goals (winning the Golden Boot), Wazza scored 6. At 18 I again scored 18 goals (again winning the Golden Boot and coming 4th in The Ballon d'Or), Wazza scored 9.
"In our opening 7 seasons, Wazza didn't outscore me once (117 goals v 80). In which time I became the 2nd youngest Ballon d'Or winner ever.
"Injuries hindered me from then on while he sustained his level. Therefore, he'll go down as a better player than me. But, at 17, please……"
Owen, 45, scored 222 goals in a 482-game club career which also included spells at Real Madrid, Newcastle, Manchester United and Stoke before retiring at 32 as injuries took their toll. He also scored 40 goals for England.
Rooney, now 39, moved to United at 18 and went on to become their record goalscorer with 253, winning five Premier League titles and the Champions League along the way. He also netted a then-record 53 times for England.
Rooney, speaking on his own The Wayne Rooney Show, said: "Me and Michael were very different players, different attributes.
"Michael Owen at 17, 18 was incredible. I used to go out on the streets and pretend to be him, I'd pretend to be Michael Owen, even though he played for Liverpool!
"Unfortunately, he did get his injuries and he probably couldn't adapt his game maybe as well as I could.
"I think his comments are fair. Of course, he's going to back himself. I'd back myself.
"But, I'd never judge myself against Michael Owen because he's someone I actually looked up to and had the pleasure of playing alongside."