Ok, so my take on the three of them is this.
Pedri is the one with the best overall vision of the game. Instinctively knows when to slow it down, when to try a decisive pass, when to dribble, when to play it safe. Weak points: he is clearly on the slow side, and he is very hesitant to shoot from great positions.
Puig has the best, most constant, and smartest movement by a clear margin. This makes him the type of player who provides a faster tempo of passing and improves the movement of others as well. A role Xavi used to have. He is easy to pass-to, thus advancing the game in a positive manner. He is quick and always looks to develop the game rather than play it safe. Weak points: his enthusiasm is uncontrolled to borderline erratic, making him a positional problem at times, especially in transitions. Weak physique.
Ilaix seems like he could be a great off-the-ball player that would join the attack and provide contributions in the final 3rd with surprise incursions (sort of like Rakitic role from MSN Barca). He is physical and doesn't demand ball to feet, but out of the three, he can have the best end product in terms of goals and shots. Also, his physicality could make him better than both at pure defensive work (tackles, handling physical duels etc.). He would be the box-to-box type.
