The Xbox One controller is fully backwards compatible to the Xbox 360 one, as it uses the very same API as its predecessor (XInput) and features the same buttons 1. It's possible you'll need to install a driver first, though Windows should automatically search for and install all necessary drivers by itself.
The only trouble you might have, is with the PS4 controller which uses a different API (DirectInput), an API which is mostly supported on older games or emulators.
As for connecting your controller to your PC, you have 3 options.
- Connect the controller using a USB cable.
- Use the Xbox Wireless Adapter for Windows 10 (sold separately).
There's also the Xbox Wireless Adapter for Windows, compatible with Windows 7/8.1 and 10.
Note: Adapters for Xbox 360 and Xbox One controllers are not compatible with each other.
- (Model 1708 or newer 2 ) Connect via Bluetooth. Requires Windows 10 with Anniversary update (version 1607, no Windows 7/8.1 support). Also works on Android.
1: The Start and Back buttons have been relabeled, but are essentially identical.
2: How to determine if your controller supports Bluetooth (Source: support.xbox.com):
Your controller has this feature if it looks like the one on bottom in this illustration:
On Bluetooth-supported controllers, the plastic around the Xbox button is part of the face of the controller. On controllers without Bluetooth, the plastic around the Xbox button is part of the top, where the bumpers are.