The approach of subset selection in polynomial regression model building assumes that the chosen fixed full set of predefined basis functions contains a subset that is sufficient to describe the target relation sufficiently well. However, in most cases the necessary set of basis functions is not known and needs to be guessed – a potentially non-trivial (and long) trial and error process. In our previous research we considered an approach for polynomial regression model building which is different from the subset selection – letting the regression model building method itself construct the basis functions necessary for creating a model of arbitrary complexity without restricting oneself to the basis functions of a predefined full model. The approach is titled Adaptive Basis Function Construction (ABFC). In the present paper we compare the two approaches for polynomial regression model building – subset selection and ABFC – both theoretically and empirically in terms of their underlying principles, computational complexity, and predictive performance. Additionally in empirical evaluations the ABFC is compared also to two other well-known regression modelling methods – Locally Weighted Polynomials and Multivariate Adaptive Regression Splines.