Publicly. I highly doubt either of the two leaders you are thinking about really believe nuclear war is an actual option. Mutual assured destruction is still a thing.

Regarding the saber rattling from current POTUS, stating our nuclear arsenal is the most powerful in the world is a non-statement. It changes nothing other than public perception of his political position. It doesn't reduce or increase the power he wields nor does it reduce or increase the power held by NK.