${[n]}_{q,q^{-1}}$ $q$-deformation

Question

It seems that in some $q$-deformations the following definition of a $q$-number is used: $$(n)_q = \frac{q^n-q^{-n}}{q-q^{-1}}$$ If we define $${[n]}_q = \frac{1-q^n}{1-q}$$ as the 'conventional' $q$-number then we have $$(n)_q = q^{1-n}{[n]}_{q^2}$$ Is there any advantage to using $(n)_q$? It seems that if it were for certain reasons to do with symmetry then it would perhaps make more sense to generalize to $${[n]}_{p,q} = \frac{p^n-q^n}{p-q}$$ As $${[n]}_{q,q^{-1}} = (n)_q$$ I haven't been able to find many papers using this dfinition however, and would like some references please. And if someone could explain the advantage, or provide insight into it, that would be greatly appreciated! Thank you