I use closed, but I live in a building with many other people in rooms around me, closed helps close out the sound from other rooms. engine noise from outside my window, etc. Often I will put on my headphones and go to sleep wearing them for the extra layer of audio isolation they provide...

I have noticed an improvement in the quality of my audio when moving from a micca origen + (a 100 dollar dac/amp combo) to the Klipsch Headphone Amplifier (a 500 dollar dac/amp combo). But the difference is negligible. However you can run into cases where your headphones may require more power...