The taxi-vs-transfer question at Kayseri airport depends entirely on where you are going. For the city, a taxi wins. For Cappadocia, a transfer usually makes more sense.
To Kayseri city center
A taxi is the obvious choice. The ride is 5 km, takes 10-15 minutes, and costs 150-250 TL on the meter. There is no advantage to pre-booking a transfer for this distance unless you need a child seat or a specific vehicle type. Taxis queue outside arrivals and you will rarely wait more than a few minutes.
To Cappadocia
This is a different calculation. The drive is 70-80 km and takes about an hour.
Taxi pros: Available immediately, no advance planning needed. You can negotiate the price.
Taxi cons: Not all drivers want to make the trip. The price is not metered — you negotiate, and without knowing the going rate, you may overpay. The vehicle condition varies. No child seat. If your Turkish is limited, communication about your exact hotel can be tricky.
Transfer pros: Fixed price known in advance. Driver meets you at arrivals with a name sign. The driver has your hotel details. Child seats available on request. Vehicle is typically newer and comfortable for the longer ride. The service waits for you even if your flight is delayed.
Transfer cons: Slightly more expensive than a negotiated taxi fare (though the gap is narrower than you might expect). Requires advance booking.
The Havas shuttle alternative
Before committing to either taxis or transfers, consider the Havas shuttle — it costs 150-200 TL to Goreme/Urgup. If you are a solo budget traveler arriving during normal hours, the shuttle is cheapest. The trade-off is a longer ride with multiple stops and schedule dependency.
Verdict
For the city: taxi. For Cappadocia: a pre-booked transfer is worth the modest premium. You have been on a plane, you are probably tired, and the certainty of a driver who knows where your hotel is and gets you there directly has real value after a long travel day.