X100 consumes noticeably more energy due to a few reasons:
First of all, constrast detection autofocus isn't very energy efficient vs phase detection.
Phase detection is basically three-step process:
1. measure differences between left and right phase.
2. look up in the focus table which distance does this measurements correspond to.
3. tell the lens to move to that point.
Contrast detection is completely different:
1. take a snapshot of current sensor state
2. compute contrast at given area (focus square)
3. tell the lens to slightly adjust it's focus distance
4. repeat 1.-3. until contrast is "acceptable" or it's the best over the range of checked values (i.e. focus hunting common to most contrast detection systems)
This usually requires numerous steps to lock up and even one iteration itself is more power hungry than simple steps of phase detection af.
Secondly, you have additional costs like EVF or liveview that is often used on mirrorless cameras. Constantly showing stream of images onto the screen bites at the battery too over the DSLR's OVF which only shows numeric values on plain energy efficient led display.
