way more energy with the speakers...

Or does it use more energy when the speakers are being used?

dementedchord is correct

because the speakers will draw current (and more current than HPs)
more energy is used
it all will produce more heat
because of inefficiencies
even more energy is used

Power amps are designed for an acceptable compromise between sound quality, manufacturing cost and heat dissipated. In a portable powered mixer, the second two parameters tend to be given more weight than in, say, a hi-fi amp.

When using headphones only, the powered mixer will draw quiescent power from the mains, virtually all of which will end up as heat dissipated in the mixer. This figure will vary with mixer type, but is likely to be in the region of 50W. If you connect loudspeakers and wind up the volume, the power drawn from the mains increases from the quiescent level. For example, if an average of 100W of audio is being delivered to the speakers, something like 200W of extra power is drawn from the mains, the difference of power being dissipated in the heat sinks and transformers in the mixer.

So-called Class-D amplifiers are significantly more efficient, delivering a much larger fraction of mains input power to the load, but I'm not aware of any powered mixers that use this switching topology other than in their power supplies.