Battery powered board-duino: external oscillator vs. internal oscillator

Does that mean the processor running at 16MHz uses an additional 4mA current compared to 8MHz? How much of that additional 4mA is due to powering the external crystal? Should I even be worry about the power consumption due to external crystal, or is that silly?

An AVR chip inherently draws more current the faster you clock it, regardless of the clock source. Another way of saying that is that there should be no appreciable difference of current draw from using the internal 8 Mhz R/C clock or an external 8 Mhz crystal resonator. There are graphs in the AVR datasheet showing the relationship of chip current draw Vs clock speed