I'll try to summarize, if you don't mind.
Imagine a 3 way speaker. That's super abstract: we have no idea about the number of drivers, shape, the bass loading (sealed/vented), size, electronics required, frequency response, directivity, distortion or anything very concrete.
Driver material, cabinet material, size, a few other things discussed in this thread and the number of ways act as a system, as the books would put it. One thing isn't more important or more dominant than another. The result of it all is what matters. With measurements you can investigate the contribution of design features and judge how much they matter. Tell me about a speaker with beryllium drivers and I'll have no reaction until you either play it for me or give me some graphs.
Generally speaking, 3 ways tend to be bigger, have more bass, show less IMD, more output and have more pronounced directivity errors, but not necessarily. Due to some frankly incredible advances in driver, baffle and cabinet design and use of active electronics we have 2 way speakers that easily outperform more traditional 3+ way designs. Think of how much was achieved with the JBL M2 and Genelec S360.