Long lived LED vs EL Wire Lamp
You have a few issues with your calculations, if you have two batteries that are rated at 170mAH at 1.5V each and you put them in series to get 3V to power the led but the capacity will still only be 170mAH (devices in series all share the same current, so any current that goes through the first battery will also go through the second). You could place the two batteries in parallel to get a capacity of 170mAH * 2 but then you would only have an output voltage of 1.5V to work with. Thus for calculating the lifetime for the LED you should be using 170mAH/10ma = 17 hours.

For the case of the EL wire you need to account for the output voltage. When you increase the voltage with the inverter the power out will be equal to the power in times the efficiency. Electrical power is voltage times current, so to have an output of .3mA at 100V (average pulled from link provided) will use .3mA*100V = 30mW of power. If you have the two batteries in series to provide 3V to the inverter it will need to supply 30mW/3V = 10mA of current. If you factor in the efficiency of the inverter it will end up needing to pull more than 10mA from the batteries so the expected life will be under that of the LED.