Air cores are not self shielding like torroids and other forms so you have to play the usual games with orientation, spacing, and shielding to prevent coupling between them.
Regarding shielding, does air core toroid better ?
Absolutely, if properly wound.
In a previous job, I studied this with both FEM analysis and experiment, with good agreement between them. Unfortunately, I no longer have access to that data, but the effect is not small. The external magnetic field of a properly wound air core toroid is much less that that of a solenoid, both in magnitude and distance from inductor center. The comparison was done on the basis of inductors of equal value and equal Q-factor. If I recall correctly, the toriodal air core inductor ended up somewhat larger than the solenoid, but the effective size of the solenoid was much larger. What I mean by effective size is the volume of space in which the energy is stored in the magnetic field. This effective size is really what determines how close you can put anything conductive close to the inductor without affecting the inductor.
What does properly wound mean? Just like the picture you show. A single layer winding with non-overlapping turns, with the gap between the ends being small. One caution is that the gap between the ends will dominate the self-capacitance of the inductor, and this will be worse than the solenoid. This is the main tradeoff, in that if the gap becomes much bigger than the turn spacing, it will increase the effective size of the magnetic field, but if it is small, it increases the capacitance and decreases the self-resonant frequency of the inductor. If using this for RF, do not overlap the ends for this reason.
Cheers,
John