Many companies require that travelers will be reimbursed for phone calls only if they are made with a calling card. Other card providers like World Telecom and Interglobe do not own their own phone lines but buy spare capacity at a discount rate from the major telecoms - sending calls along the cheapest and most reliable route. Then there's the question of line quality because some calling card companies reduce costs by ''compressing'' calls to get more on a line. The reason is you get a better call quality using a fixed line and there's less risk of a call dropping out midway through. Business people use audio-conferencing more and more and calls tend to be fairly long.
Some cards have a call-back facility to avoid high local, or hotel phone, charges.
There is no overall cheapest calling card. It has the advantage that it avoids value-added tax on calls that originate outside Europe. This avoids exorbitant charges of having calls routed back through your home country. In some countries you can buy prepaid cards for your mobile that allow you to make and receive domestic calls. You pay slightly more than the local mobile rate.