I having issues with the EL light, it not bright enough when using the inverter with Arduino.
I have connect a separate AA battery pack to it but it also isn't as bright as the direct battery holder.
Your schematic atells a lot. The transistor you state in your question will drop the 3.3V by 0.7 volt. The MOSFET will work much better as you show in your schematic. Try adding a few uF and 0.1 uF capacitors from the Source (ground) to 3V3.
2 AA batteries give 3V and Arduino i tested with 3.3V and 5V. Comparing the 2 different inverters with and without the battery holder are they the same or different? The AC output voltage is very different. Do i need a current/voltage booster circuit or a different inverter.