Dybala penned a new five-year deal with Juve on Thursday, two days after putting Barca to the sword in Juve's 3-0 win in the Champions League quarter-final first-leg clash.
That put to bed any talk of a departure from Juve and Dybala believes the Turin club are on the same footing as Barca and their Clasico rivals, as well as Bavarian giants Bayern.
He told TyC Sports: "It's the best moment of my career. I feel really good on the pitch, I'm at a club that has nothing to be envious of Barcelona, Real Madrid or Bayern Munich about.
"The fans, my team-mates and the club have made me feel like this. That's why I had no problem renewing.
"This club competes for all the tournaments it takes part in, it's the biggest club in Italy and from the moment I arrived they have helped me to become aware that we have to win everything we play for, against any opponent and on any pitch."
Dybala suffered an ankle injury in Saturday's 2-0 win over Pescara, but the Argentine is confident he will be fit for the return leg at Camp Nou on Wednesday.
He added: "I had normal training with the group on Monday, but I didn't do the last part of the session out of precaution. But I'll be at 100 per cent on Wednesday."