I don't really care about CoD, other than recognizing its place and impact on the gaming scene. Having said that, I have a 16 year old nephew that's a hardcore CoD player who is playing on both systems, and his opinions, (and the opinions of his friends,) seem to mirror yours exactly, OP. I sat down with a bunch of them this weekend. It was my first time to see both systems in person.
I wasn't surprised about the resolution making a difference, as I recall my experience playing PC shooters -- going to a higher resolution having a positive impact on my play, especially sniping, where as long as the draw distance is the same, higher resolution simply allows you to pick out far targets a bit quicker. Nah, I was surprised these kids like the DS4 so much. All of them preferred the 360 controller before, and none of them picked the XBone now. Unlike your stick complaint though, I've heard more complaints about the XBone bumpers from these CoD players.
There kinda is a downside to this, at least for me. In the past, I've gone over to my sister's place and my nephews and their friends were usually on the 360, usually playing CoD, leaving me plenty of time to play PS3, which was always on the better TV, in the home theater room. That has definitely changed. The PS4 is the one they are choosing for CoD, so I didn't get nearly the time I'd hoped for to play Resogun.