If soil support of a continuous footing yields, all the soil particles move parallel to the plane which is perpendicular to the center line of the footing. On the other hand, if the soil support of a square or circular footing yields, the soil particles move in radial and not in parallel. So bearing capacity increases. 

It is probably related to the volume of the mass under the footing that needs to be displaced to lead to failure and it's moment of inertia relative to the footing centerpoint. 

In this case the value of terzaghi capacity factor same is Nq even use different footing this because Nq reflects to influence of surcharge or working load. But for Nc and N gammar is different because Nc reflects the influence of the soil's cohesion on its bearing capacity and N gammar shows the influence of soil weight and foundation width or radius.

The failure will occur in accordance with the narrow side of the footing. Therefore circular footing, without preference for specific failure direction, is more "cost-effective".

because of axisymmetry

It is simply because strip footings engage smaller mass of the soil and it becomes 2 dimensional problem(plain strain) whereas for circular and even square footings, the soil mass contributing to the shearing resistance comes from the three dimensions there for much more pressure is required to displaced the soil particles due to 3D effects

If we compare this two situations: 1) isolated square footing and 2) many square footings  placed adjacent together in a row acting like the strip footing, we can see that the stress under the isolated square footing must be less than stress under square footings in a row because of the stress interference from adjacent footings. On the other hand, even though the same width of footing, if the soil under footing of two cases above get the same stress level (e.g., the shear strength)  the applied load of case 2 must be less than case 1. So the circular and square footing have more bearing capacity than strip footing.

I think the most important issue here is to compare the shapes OF THE SAME AREA. In this case, due to the specific perimeter the largest settlement and the least bearing capacity will be recorded to the round shape, while the rectangular shape behaves better. To understand better see I. Cherkasov's contributions in the field of foundations on loessial soils. Of course the things are different if you compare incomparable things (such as foundations of different stifnesses, areas and so on) or if you have improper formulation (2d plane strain, plane stress or axial symmetrical). So, in a nutshell: the worst behavior is for the round shape if you have the same area and stiffness of the foundation, but you cannot compare a round raft with a continuous footing.

Dear Debasis.

in my opinion, for case of strip footing the failure occurred external side side of footing. however, the failure of circular footing has occurring a long period.