Xbox 360 controller has a wired variant which is a huge plus, and works well all around.
Xbox One has micro-USB wired mode, which if you want to fix certain games (PSO2, Azure striker gunvolt), but the port on the top is a bit janky.
I reccommend the 360 controller, but if you are interested in the One Controller, definately go for the Pro or Razer Sabertooth