The problem with questions like these is that not all 2-ways and 3-ways are created equal. There are high end 2 and 2.5-way speakers that can do everything better than 3-ways employing lower quality parts and materials.
Some 2-ways like the aforementioned Fritz speakers can sound more refined and play nearly as loud, or even louder, than many of the common $5000/pair 3-way from the likes of Revel, KEF and Paradigm.
IMHO, most 3-way designs, especially those under $10K/pair, don’t actually capitalize on the theoretical advantages of the design. Perhaps some of the newer value leaders from Arendal actually do, but then I wouldn’t be surprised if speakers like the 2-way JBL 4367s perform better subjectively.
The more experience I gain with DIY modding and building of speakers, the more I am becoming convinced that a speaker’s driver quality is what matters most. I would take a 2 or 2.5-way with some properly implemented Satori Textreme drivers over nearly any 3-way I’ve heard from the major manufacturers.
A speaker like this will slaughter many/most 3-ways under $10K/pair: