I haven't tested it out myself, but both are advertised to run about 12 hours.

The E01 is brighter and uses up more power than a Photon, so that's one reason.

A common alkaline AAA is bigger than a coin cell, but lithium batteries have a higher energy density than alkaline batteries and coin cells are usually lithium batteries. In addition, two stacked coin cells also results in a higher voltage than 1xAAA (6V vs 1.5V nominal), so less current is sucked from the coin cells to generate the same power at a lower voltage.