It all depends on the context, which you haven't included. In its simplest terms, a "quantitative basis" relates to how much there is of a particular item. So, in making a choice on a quantitative basis, you have to specify what it is that you are measuring, and whether "bigger is better".
For example, let's imagine that we are asked to choose between 2 cakes. I, being a greedy individual, would choose the bigger cake. You might be somewhat allergic to nuts, so you would choose the smaller cake with no nuts in the recipe. Both of us are choosing "on a quantitative basis": me on the basis of dimensions (and bigger is better); you on the basis of the presence of nuts in the cake (and less is better; none is best). In choosing on a purely quantitative basis along these particular parameters, neither of us take taste (more difficult to assess on a quantitative basis) into account.