Ronaldo left Real Madrid for Juve in a €112m deal.
“I'm surprised that he would leave Real Madrid and go to Italy," Giggs told ITV Sport.
“He's obsessed with being better than Messi. He has that now that: 'I did it in England, I did it in Spain, I'm going to do it in Italy... and I did it with Portugal'.
“So maybe that will be his argument when people ask: 'Is Ronaldo better than Messi?'."