Not much. The triggers can now vibrate to give feedback, but I don't know if any PC games do (or even can) implement that. It also feels different. I don't like the feel of the new design, but the majority of people seem to agree it's more comfortable than the 360 controller.
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On the other hand, 360 controllers have gotten cheaper if you just stick with those. Does the XB One controller add much?
Not much. The triggers can now vibrate to give feedback, but I don't know if any PC games do (or even can) implement that. It also feels different. I don't like the feel of the new design, but the majority of people seem to agree it's more comfortable than the 360 controller.
Microsoft did spend $100 million developing the new controller, so I hope they've got some improvements to show for it. I haven't used it much myself.