Conte vs Allegri
It's hard to say who plays the better football as i think both are still very young coaches and both are evolving their ideas. Conte was very set in his ways at Juve and he softened his approach a lot when he joined Chelsea. He's become more open and flexible. The same applies to Allegri as well as he's shifted from 3-5-2- to 4-3-1-2 and then to 4-3-3 and others. I think Allegri perhaps plays the better football on the basis of his 3 seasons at Juve - this season, his ideas are taking time to take root so we may not see his best football at Juve until February/March.
Allegri has a good policy with youth, although he prefers to go with more experienced players at the moment because Juve don't have a lead in the table and they don't have the room to experiment like in previous seasons.
I prefer Allegri over Conte, simply because he is more laid back and able to change his ideas, depending on the situation. Conte was always a little too keen to work the players too hard and run them into the ground, but he is a superb motivator.
Views of the brilliant @juvefcdotcom