I am a new 2014 Prius C3 owner and I would like to find out if Xenon or Blue Headlights are recommended or safe. Or if not, What is the best headlight.
"Blue Headlights" are illegal everywhere in Europe and North America. Generally those are HID (Xenon) with a high colour temperature (5000K-12000K). HID Headlamps are the best on the road. LEDs are coming close, but still not there in terms of luminous output. But LEDs win in terms of "bulb" life (there is no "bulb") and energy consumption is marginally better generally. Your Prius C probably came with halogens. This means you can only put in halogens or else too much light will reflect above the cutoff and you will blind oncoming drivers and yourself in the heavy rain/fog/snow. If you want to do it right, retrofit some good HID projectors into your reflectors.
I believe the lexus RX350 projectors swap right in. Or with little tweaking. The halogen projectors look like mini RX350 projectors.
I believe the OP is asking about halogen replacement bulbs with a blue glass capsule or coating. These are mainly for looks, actual on the road illumination is in the 4300k to 5000k color temperature. Which is warm white to white. Any blue coating will decrease the light output of the bulb. SCH-I535