why the heck would you ever cold boot? That's a moot point as you should always have it on quick start. The Store takes about 3 seconds. Not slow. I can't comment on elements of the UI in comparison as I haven't used a PS4, but the instant swapping and snapping is pretty fast.
Maybe your TV is set to too high a sharpness because I don't see very many jaggies in KI.
I think if you use your 360 controller again and pay attention you may realize that it too needs pressure on the outside edges of the bumpers, and that's how most people actually press them.
The Kinect should already have a super wide vision - so wide that it can see all of your room. Where are you sitting? You should be able to manually tilt and calibrate it to where you normally sit.
I cold boot on PS4 because it takes mere seconds to do so (SSHD). I don't want to leave the XB1 in standby because it has crazy power consumption to do so. There's no reason why a cold boot should take so long. My Panny 50" VT65 plasma is calibrated and sharpness set at a minimum setting, there's no problems there. I still prefer the 360 controller to both DS4 and XB1. And how does 'super-wide' help with the fact it can't see in 'super-tall' vision. I'm 6'2" and I need to stand well back for it to see all of me.