I'm chilean and watch alot of Juve because of Vidal, big fan of him. I'm also a fan of Colo Colo, the club at which he started in Chile, so I've watched him for the last 8 years of so. I think if you swapped him for Yaya it would be a bad choice. They are different players - Yaya is a deeplying playmaker, I think he is techniclly better than Vidal and has better passing. Vidal tackles more and is much more aggressive when recovering the ball.
In Juventus, where Vidal is the best player of the serie A, they play with a 3 man midfield - Pogba, Pirlo and Vidal. Marchisio rotates. The deeplying playmaker is Pirlo. That allows Vidal to attack and have alot of freedom when going forward. Many of his goals are in a forward-position. He doesnt score as many goals from outside the box as you'd think. Most of them are inside the box. In a 2 man midfield with Fernandinho, things would be very different for City's playing style. It would be a much tougher midfield, since Yaya has been losing his defensive skills, but you'd probably lose some precision when passing.
In Chile he plays in a 3 man midfield as well, along side a deeplying playmaker like Marcelo Diaz and another defensive midfielder which allows him to attack freely like at Juve. He's having the best moment of his career in the national team. With him and Alexis Sanchez, we hope to surprise Spain and the Netherlands at the WC in June.
I think Fernandinho, Vidal and Yaya could probably play together. But I dont think he would work alongside Fernandinho by himself. Maybe along Yaya, but then he'd have many more defensive duties and would probably not score as many goals.
The other good thing about Vidal is that he can play almost anywhere on the field and that is great for a coach because of suspensions/injuries. In Chile he's played as right center back, left center back, libero, defensive midfielder, offensive midfielder, on the right, on the left, and he plays well everywhere. In Juve a couple of matches ago he played as RCB and did an awesome job. But he's probably too good to play as a defender.