When the game was tied (either at the beginning of a game or after a goal was scored to make it tied), the Coyotes got the next goal 9 times and Chicago got the next goal 6 times.
When losing, the Coyotes got the next goal four times and Chicago never scored with a lead. I think this was very crucial in this series -- Chicago never got a two goal lead.
When winning, the Coyotes were not great. Through game five, they scored the next goal only once and the Hawks scored the next goal six times. But they evened it out in game 6, scoring three goals with a lead, making the final total 4 to 6.
Phoenix actually played with the lead for much longer than Chicago -- 117 minutes to 58. In other words, when Chicago got a lead, Phoenix tied it up quickly, but when Phoenix got a lead, Chicago tended to take their time before tying it up.
In short, Phoenix was dominant when the game was tied and when losing, outscoring Chicago 13-6 in that situation. They were less than stellar with a lead (which is actually pretty common in the NHL playoffs). The series may well have been won because three of the times that Phoenix took a lead, they didn't have to defend it because the game ended instantly.
The other number that really sticks out to me is Chicago's power play, which was 1/19. As well as they buzzed our net even strength and given how seemingly easy they scored on all three of their 6 on 5s with the empty net, it's hard to understand how they weren't better on the power play.