I make the transition when I find a repair tool. Before that point, the difference is too small to bother, give up the universal tool and fill another inventory slot.
At that point, I am already able to craft iron pickaxes surpassing the stone ones and able to swing them continuously.
Not considering amount of mods as well as very unlucky stat rolls, as such early abundance of the former and occurence of the latter are edge cases.
I perceive both of them being in a their own good spot. Steel on the other hand...