the big advantage of a folded cascode is its larger outputswing. And as you know the more signal range, the higher the SNR. Unfortunately you have more branches between Vdd and Vss, and therefore the folded cascode dissipates more power. However, as Vdd decreases more and more, telescopic opamps will more and more dissapear.
If you use not a 2nd stage, this opamps are otas and are used in SC design for instance.
When Vdd decreases , telescopic hasnt enough voltage room for large output swing and folded cascode may still can . Besides, folded cascode has large input range than telescopic
but folded cascode dissipates more power because of more branch, and also folded cascode are slower than telescopic because of more parasitic capacitance at the folded node