With the new Xbox One Experience, Xbox team have added button remapping capability for standard Xbox One controllers through the new Xbox Accessories App. This allows each user on the console can have their own custom button mapping instead of remapping buttons on an individual game basis.
Standard controller remapping can be accessed in three ways through the New Xbox One Experience:
- Settings / Kinect & Devices / Devices & Accessories
- Settings / Ease of access / Button mapping
- Launch the Xbox Accessories app directly
For standard controllers, you can now swap button pairs. For example, if you choose to map LB to X, then X is automatically mapped to LB. This maintains that all buttons are always mapped on a standard controller.
Read more about it here.