Both have their place and I usually treat a slab as 2 way if possible or if the slab is going to function as one unless it is small and there is no benefit.
Briefly:
There are a couple of types, those supported by columns and those supported by a fairly rigid beam/wall system.
The advantage lies with the latter; it is possible to reduce the slab thickness, reduce the amount of reinforcing within the slab (even with the increase in top reinforcing, because it's often required anyway), and reduce the cost. It is also possible to increase the overall stiffness of the slab. This is applicable only if you have supporting walls/beams already; to construct them specifically for support is more costly and the benefits are lost.
The important considerations are the edge support conditions, the cost of the additional support structure if required, and the quality of the labour or documents. This type of construction requires a better skilled workforce.