I have a tough beard and sensitive skin. I spent many years evaluating more than 100 soap formulations (more than 250 soaps) from numerous producers, both traditional and artisan. I was looking for soaps that are easy to load, easy to lather, provide exceptional slickness, both primary and residual (slickness remaining after visible later is removed), provide skin protection to minimize skin irritation from the blade, and finally, to leave my skin feeling smooth, moist and conditioned for many hours after the shave.
Most of the traditional formulations failed to provide what my skin needed. The only two traditional soaps that came close to being sufficient were Mitchel's Wool Fat and Tabac tallow formulations, but both of these soaps have been reformulated and I have not tried the new versions, so I cannot recommend them.
My favorite soaps are from Grooming Dept, now marketed under the AION Skincare label. The Maxima, Mallard, Optima and Kairos SE formulations are phenomenal. These soaps represent nearly have the soaps in my rotation of 75 soaps. Other soaps that are good enough to remain in my soap rotation (in alphabetical order) are:
Ariana & Evans K2e formula
Barrister & Mann Omnibus formula
Declaration Grooming Milksteak formula
Ethos Grooming Essentials F Base formula
Gentleman's Nod Cardinal formula, especially C4+
House of Mammoth Tusk Formula
Murphy and McNeil Kodiak formula (AON is almost as good)
Noble Otter most recent formula
Oaken Lab V3 formula
Wholly Kaw Siero formula
Zingari Man Sego formula
Although I have tried a lot of soaps, there might be soaps I have not tried that are also excellent. However, do not expect a soap costing less than $20 per 4 ounce tub to preform as well. High quality skin care ingredients are expensive. However, high pricing does not guarantee superb performance. I have been disappointed by some expensive soaps like Saponificio Varesino, although some shavers love it. My evaluations are from the perspective of someone with sensitive skin. Those who have oily skin might not agree with my listing. Those whose skin is oily might not need the skin conditioning I appreciate.