I have three bikes, each with different tires. I ride them all in similar conditions.
I have 2500 miles or so on a set of Armadillos. No flats. But as others have said, it's a hard-riding tire. They don't seem as quite grippy as the other two.
I have 2500 miles or so on a set of Continental Ultra Gatorskins. One flat--a chuck of safety glass stuck to the front tire in the rain. These tires are very comfy riding and quite grippy.
I have 650 miles on a set of Bontrager Race-Lite Hardcase. No flats yet. They seem as comfortable as the Contis and just as grippy. They don't seem to be getting cut up faster.
Around here where glass and metal bits are the primary puncture hazards, (no goatheads) I'd be hard-pressed to decide between the Contis and the Bontis.