As far as I am aware, the selection of the best ligands for transition-metal catalysed reactions is still trial and error. In fact, not only is the selection of ligand trial and error but so is the choice of starting materials to result in that metal–ligand combination.
What the original discoverer of a reaction method typically do is run a number of screens keeping most parameters constant but varying one; this one varying parameter will be ligand, solvent, time, temperature, additives and metal salt. (Usually, they will have decided before running the experiments which metal they want to use for their reaction so the only reason to include another one is to directly compare the new method to an existing one and e.g. show that nickel is better than palladium in this reaction.) Whichever reference you’re looking at, the authors most certainly performed such a screening and received a slightly higher yield for one set of reactants compared to another; they then published that as their final choice.
After having found the optimal conditions, many researchers are tempted to ‘explain’ why a certain ligand is better than another ligand. Our knowledge does include how electron-rich or electron-poor the donor atom of a given ligand is, how sterically demanding a set of substituents is and so forth. If ligands of one general type form a general trend, one could well be tempted to draw from that general trend and exclaim that e.g. an electron-rich phosphane works best for this reaction. In ideal cases, that prediction is then tested experimentally with a previously unused but more electron-rich phosphane; a reaction that may or may not work. The point, however, of this paragraph is that more often than not the ‘explanation’ is little more than a post-factum rationalising ballpark and should be treated as such. Years to decades of research will likely be required until we actually fully understand the intrinsic properties at play and are able to make good predictions.
