Changing power types is inefficient.

Batteries (which is what your emergency power supply uses) and solar panels are DC. They will be most efficient powering other DC devices directly.

Rotating generators (powered by engines, turbines, wind, anything that creates movement through motion pretty much) are AC. They will be most efficient at powering AC devices directly.

As soon as you’re changing DC into AC, or AC into DC, you’re losing power (usually a quite significant amount) in the conversion process. DC->AC requires an inverter. DC->AC requires a rectifier. Both are inefficient.

The direct answer to your question is that your DC power bank will be most efficient powering DC devices, and less efficient powering AC devices.