Let \(\widehat{\mathcal{C}}\) denote the category of coherent functors on a category \(\mathcal{C}\). Suppose that \(\mathcal{C}\) and \(\mathcal{D}\) are additive \(k\)-categories and that \(F,G\) is pair of adjoint functors between them. The author obtains comparisons of \(\text{ gl.dim}(\widehat{\mathcal{C}}) \) with \(\text{ gl.dim}(\widehat{\mathcal{D}}) \) under various natural conditions on \(F\) and \(G\). These results are then applied to compare the global dimensions and representation dimensions of Artin algebras. In particular, if two Artin algebras are obtainable from one another by switching, then they have the same representation dimension.