Does the infrared heater perform better than fan heater ?

This is a matter of personal preference. The Infrared heater will give you instant heat sensation on your skin. It works with no needs of preheating. Fan heater raises the air temperature in the room firstly. When you are taking a bath and the air flow  from fan heater comes to your wet skin, you will feel cool or cold. If you intend to use a heater for a bath, the infrared one is definitely suggested.