This not how simultaneous side-stick input works. Conflicting inputs are rejected with a warning ; dual input is also indicated with a warning. Non-conflicting inputs are summed, to model the way traditional centre sticks/yokes would work, when both pilots are acting. Generally, due to procedure, only one pilot is controlling the aircraft at any time; and, there is a "hand-off" to pass the control between them. There is a priority override button on each side-stick to take control from the other pilot.

However, a potential problem with side-sticks arises because the sticks are independent -- the non-controlling stick does not mirror (i.e., no force feedback) the controlling stick movement, as would happen with the mechanically connected centre sticks/yokes. Meaning, the non-controlling pilot cannot tell what the controlling pilot is doing.

This was the problem on AF447. If you read the CVR log, one pilot was confused about how to handle the situation and, unfortunately, he took control several times during the recovery attempt. In the final seconds, he verbally states he is pulling back on the stick (attempting to climb), which revealed to the [then returned to the cockpit] captain what he was doing, but there was not enough time to correct (forward, nose down) to exit the stall before they struck the ocean surface.

(The stall warning itself was another disastrous UX problem as well, in my opinion.)