I have no idea why I'd want to use my phone instead of a card.
There is also some potential increase of security:
Unlike (nearly) every card(*), the phone is a device that has its own display and input interface.
Meaning that you don't need to trust the payment terminal(**).
- No risk of skimmer trying to read you PIN: you're typing it into your own phone, not on the terminal which could have been hacked/modded.
- You can trust the amount displayed (again, you are reading your own phone's screen, so even if the terminal is hacked to display a lower sum and actually bill a higher sum, you'll notive the discrepancies).
Also, the phone has connectivity, which allows out-of-band confirmation for the transaction (***).
Thus, the device is protected against fraud that could menace a classical card.
- hacked terminals showing bogus transaction amounts, or trying to record your PIN.
- hackers trying to relay a transaction (small amount are "tap/swap only": no signature neither PIN asked. It's possible to use a powerful antena pointed at a wireless credit card to remotely use it and relay communication to a terminal).
Saddly, the phones have their own problems:
- they eat batteries like candy (even wireless credit card transaction are remotely powered by the terminal. Whereas a dead phone is dead and can't be used for paying).
- again, they are conencted. Which means that they could be compromised themselves. (Specially since people tend to install tons of crap).
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(*): I've seen banks issuing cards used for e-banking that have a build-in screen and keypad. Similar devices are in theory possible on a credit card.
(**): lots of e-banking card reader do exactly that: you can check on the screen what you are asked to sign.
(***): That's a security feature that's also offered by combining classical credit cards and separate connected device. I can be asked to confirm by SMS / by voice call when the bank detects unusual traffic on my credit card.