Taxis are a nightmare as they can charge whatever rate they feel like, don't have to be licensed and can just stick a sign on their roof and be ready to go. As you come out of Budapest airport go to the Főtaxi box which is outside arrivals. Passengers of Főtaxi receive a ticket stating the maximum fare. When you get in the taxi the meter is on and if the amount upon arrival is lower than the sum officially given for the zone, you need only pay this amount if it is higher, tough you pay the amount on the ticket.
These are the rates when we were there in March/April
Prices are equivalent to Tenerife, but Vienna if you do a detour is horrendously expensive - need a mortgage just for a coffee.