I've used both CHT and Far Eastone - the latter was a better deal for my month's stay, but only when purchased at the airport. The airport location (arrivals level, down the hall from the bus station) offers the best deal - 30 days of unlimited data and NT350 for outbound calls for a total of NT850.

My Galaxy S4 was able to get HSPA almost the entire time throughout Taipei and New Taipei, and by running Talkatone all the time, I could receive and make calls back home for free and the voice quality was perfect over the FET data network. My friend bought the card for me at the airport, so I don't know about ID requirements at the airport, but when I bought another card for my other half later in the month from an in-city location, I had to show my passport and drivers license (both were copied) and the deal for the card was much worse - NT350 for 8 days of data plus NT300 deposit to cover voice calls (optional).

Taiwan passport holders need to present their passport and Taiwan National ID card when getting a prepaid SIM (even if they permanently reside abroad and just visiting TW), so be aware of that if visiting back home and need a prepaid SIM. Foreign passport holders need their passport and one additional government issued photo ID.

I don't know why governments in Asia are so keen on collecting and storing personal information of phone users (visitors to Korea can't even buy a prepaid SIM) - here in the US you can buy a prepaid SIM without any ID or hassles...Straight Talk even offers vending machines for SIMs and phones at many airports.