Well, for what my buddy had time with both controllers.
He says they are both equally great. The X1 controller has more precise movement, that the smaller thumbsticks, but better grip to it and easier movement makes it perfect for practically any type of game. They got rid of the horrid Disc-Shaped D-pad from the X360 Controller to something more traditional, the X1 D-pad is more indented into the controller so to say. Instead of sticking right out, it's into it more so your thumbs don't slip out of place if in a fighting game. Like KI for example.
Triggers are great, more natural placement for your index fingers, rumble motors inside them...well he didn't get a chance to test those.
Buttons are closer together to make it easier for things that require A+B combos, faster button tapping so to say.
Now, The PS4 controller is wayyy wayy wayy better than the past dualshocks. He didn't give me much detail on the PS4 Controller, the only thing he said was it's bigger and not as...well weird on your hands for shooters. He didn't mention the speakers inside the controller, but the LED light on the back of it wasn't working, kinda flickered then stopped shining, triggers are once again improved!

It's pretty awesome.
But if he were to choose, he'd chose the X1 controller over PS4, since...well he's more obsessed with actual facts and not well interested in PS4.
Me though? X1. It's more natural to me, I don't know why. Though it'll be hard to get used to.