The X1 sticks are universally better liked, and the rubber won't peel like on DS4 sticks.
EDIT: An earlier version of this post recommended disconnecting the LED light on the bottom of the controller. DO NOT DO THIS. The cable that connects the LED light also connects the battery to the battery charging cable. I took out that step in the updated version.
Bonus: I'll also detail my experience trying to use X1 sticks on the PlayStation (PS) Vita. It didn't really work, but I'll detail it all the same.
STEP 1: Get your gear. The only tool you'll need is a tiny little screwdriver (and maybe a pair of needle nose pliers if you screw up your ribbon connections like I did). You'll also need X1 analog sticks. I used these. They are NOT exactly the same as the real X1 sticks, but they're a bit cheaper and less grippy. They're a definite upgrade for the DS4, and they fit. Also it's these or nothing.
STEP 7: Put the top half back together and TEST ALL THE BUTTONS. The web browser search window is the fastest way to do this.
If you're like me, this is where you'll realize that the touchpad is broken and have to go back and fix it. For example:
if your trigger doesn't work, go back and jiggle it around until it does.
Make sure the Options and Share buttons are installed.
BONUS! Installing Xbox One Analog Sticks on the PS VITA
You'll need these little Vita button covers, and some Gorilla glue. I would not recommend gluing the sticks directly to the Vita because you might not like them.
STEP 1: Identify the problem. The Vita is not exactly designed for ergonomics, it's designed to fit in your pocket. These little analog sticks are OK for turn-based games, but terrible for first-person shooters and action games. If you're like me, you stupidly planned a vacation for September, and your only option for playing Destiny for two weeks will be Remote Play. So let's try to improve those sticks.