Does a wireless Beats headphone use more energy than a wired one?

I'm wondering whether a wireless (bluetooth) Beats Solo 2 headphone uses more energy than a wired one, for example the Solo 2 headphone.

I'm asking this because I would like to buy one.

On the one hand I think the bluetooth one will use less energy from my iPhone because it uses the energy from its own battery inside the headphones to produce sound. However, my phone has to establish a bluetooth connection, which also uses energy (but my bluetooth is always one due to my Apple Watch).

On the other hand I could think of the wired one that uses more energy, because this one connects via the 3,5 mm jack and this wired headphone doesn't have its own battery, so all the music that is produced will use energy from the battery of my iPhone, so this could take more energy.

I hope someone can answer my question!