Forget the blower/fan for a minute.

OTEP's answer sheds some light as to exactly HOW an aircon compressor works.

Moving the thermostat actually just influences how often and how long your compressor's clutch is engaged. A high cooling setting means the A/C compressor clutch is engaged for longer periods of time before it stops, although it will have longer breaks. The reverse is true for a low cooling setting (more frequent breaks but shorter engagement periods). If you're observant enough, you can actually HEAR the clutch engaging and disengaging.

Since the clutch is engaged longer on a high cooling setting, you burn more fuel...but regardless of what position your thermostat is in (or even if your A/C is on or off), your compressor will still be spinning every time you run the engine because it's connected via a belt.

So now you know WHY the second option is easier on fuel.