Xbox – Does the Xbox One controller have pressure sensitive triggers

The Xbox 360 controller does not have pressure sensitive face buttons. The only pressure sensitive inputs are the analog sticks and the triggers. The issues this causes for games developed for other platforms is a common complaint - notably Metal Gear Solid games, as you've mentioned.

Wikipedia even mentions this in their article about gamepads:

[On the Xbox 360 controller,] the pressure-sensitivity feature on the face buttons was removed, making some original Xbox games, such as Metal Gear Solid 2, unplayable.

Simply, you cannot. The battery packs in the xbox one's controller and the 360's controller are shaped very differently and are not compatible with each other.