Although a battery might say it is 6 volts it might have a higher voltage. This is a problem is your device is sensitive to too high voltages.
Running off the USB cable the Arduino Due can generates 3.3v and 5v.
Running off the USB cable the Teensy 3.6 can generates 3.3v and 5v.
Below are two voltage regulators. The first reduces the battery 6 volts to 5 volts.The second reduces to 3.3 volts. The issue with voltage regulators is that the unused voltage is converted into heat. Thus heatsinks are useful.