This is not an option where you can choose which connector you like better or which one you still have free from the power supply. You need both connections for the card to work properly.

As @Brimstone mentioned, you need both connectors! With only one of the two connectors, you will get a message on the
screen telling you that you have to plug them both in ;) Greetings Fabio

Unfortunately, only the 6 pin is not enough, at least the 8 pin is needed so that it can draw enough wattage on the standard clock.