I guess I should clarify, I have not tried vintage Williams, so I am talking about the current formulation.
Palmolive soap or cream - loved by the whole world, except me! I cannot get a decent lather that works for me. Sub-par performance and boring, albeit nice, scent.
Ogallala Bay Rum. It's finicky about water. A little too little, it dries up & clogs the razor, a little too much & it breaks down.
Arko makes my face burn. Slick, but not worth the irritation. At least I got a tub to use with my Stirling samples though.
Arko is a no go for me. Besides the urinal puck scent, it burned my face and turned it red. It lathered like crazy, but no go for the burning. I also didn't like the Glacial Sterling I used. Its finicky for water, and the Glacial numbs my face to the point that I can't feel when the straight razor is about to bite.
OK, here is a shaving soap heresy-and-a-half wetshaving forum style: I think there are some non-tallow soaps that are every bit as good as the best tallow soaps. Institut Karite for one, and also The Soap Opera Himalaya and Van Der Hagen Deluxe.
I did that and got substantially improved results. I first tried Williams when just starting traditional wetshaving. It produces a rather watery lather with large bubbles. That turned out to be my fault, not the soap's. When I tried Williams again years later with the same brush, it worked rather well. Not great, but still well enough to get a good shave. After running out of shaving soap a couple days ago, I found a small local pharmacy that had Williams for $1.21 a puck. Using a horsehair brush, it lathers very well, but the later disappears soon after I apply it to my face. Nothing to worry about, though. If some soaps do not work well, there are plenty of others out there that work fine.