With 3D Secure, you provide the normal card data (i.e. card number, expiration, name, CVV/CVC) to the merchant and are then redirected to an authentication form from your card issuer. There, you'll be asked to either provide a password or, as you described, input a confirmation code from a text.

With Sofort, you're entering your login data to your e-banking account on a login page served by Sofort. They, in turn, use it to log in to your e-banking using a simulated browser and send a wire transfer. You lose control, however, of what else they do: once they are logged in to your e-banking, they can check your previous transactions, send other transfers or they might change your mailing address...