My issues with Phoenix Sky Harbor notwithstanding, Delta isn't a horrible way to go when in Phoenix. Of course, they're not a main carrier in this airport, but because they're a major carrier and so ubiquitous across the U. S. of A. they don't get treated like a redheaded stephchild here like other carriers.
I didn't check bags this time, but in occasions past they haven't had any problems with them. Gate agents are just fine--somewhat robotic but in the efficient way. That's not mean to be a backhanded compliment, they just do the same thing over and over and I haven't had any issues with them.
You're probably flying US Air or Southwest into Phoenix, but Delta is doing their thang in PHX, and doing it just fine.