The only certain way to know is to try it.

However, my math says this: Bluetooth radios use about 35-40ma of current, which is roughly 120mw, when transmitting or receiving.

The latest iPhone is reported to have a 3 watt speaker. In my experience, audio amplifiers have an efficiency of roughly 50%, worst case.

If you compare a maximum of 6000mw to 120mw, the speaker seems to use more current, and therefore drain the battery faster. OI course, this is Just based on the math; it would take some dedicated testing to determine which actually lasts longer. Still, if I had to bet, I’d bet that playing the speaker at full volume will kill the battery first.

Of course, there is the third option: using a wired amplified speaker or external DAC. The input impedance on those is around 1000 ohms, and with a nominal output voltage of roughly 1v, that is around 1/1000 watt, or 1mw of power draw. So if you want the most efficient playback method, grab an aux cable and plug in to the headphone jack.