That's a great question! There will be a difference in the sound quality due to the audio compression through both forms. Also, one option is wired and the other is wireless audio streaming.
Also, depending on the headphones, you can listen using the cable with the headphones either turned on or off, you don't need to have them turned on to get sound. However, if you turn the headphones on with the wire, you will often get the benefit of our signal processing and EQ to deliver the signature Bose sound!