As a rough estimate for the behaviour, I have plotted a graph.
Taking a slice of the loop, the field from the left and right current elements fall off like 1/r^2, here I have modelled the graph such that r is radius of the loop, and x is the displacement from the origin.
See how inside the loop, the magnetic field is actually weakest in the center, and approaches infinity after we reach the radius of the loop
Outside the loop, the magnetic field falls off rapidly, which is the expected behaviour.
The behaviour of this graph is for infinitely thin currents, however I believe the generalisation to volume currents is similar, with this function having a domain restriction once we reach the wires radius to avoid infinite magnetic fields.
I could be wrong, but I am fairly confident that this is a good approximation (obviously ignoring there is a full circle, not 2 current elements). Focusing on the rough shape, and not the actual numbers atleast.