I've used tallow-based soaps for a very long time. Recently, I decided to switch to vegetable/vegan soaps. My experience with them is limited. The best soap I've used thus far is the Tcheon Fung Sing Linea Intenso soaps. I also ordered some "Soap Commander." Recommendations welcome.
Proraso Red for the post shave feel, PAA is also great especially anything with the Crown King formulation it feels like a Tallow soap but it’s not. Caties Bubbles is also pretty good with amazing scents Sent from my iPhone using Tapatalk
Xpec cream if you don't mind a soft soap. It is really a croap. I recommend you get the unscented, as many people hate the scented version's scent. Right now, for performance, xpec is my favorite out of any soap or cream, those with tallow included. It is expensive, $38 shipped to the US from Connaught Shaving, but it is worth it. Slickness and cushion are top notch and the post-shave skin feel is the best. If you prefer a hard soap, or if you want good scents, I suggest Saponificio Varesino and/or Wet Shaving Products (their vegetable line is called Rustic and there are lots of scents to choose from).
Not experienced enough to say that I have a "favorite".... But, I really like Wickham Soap Co. "1912 Russian Leather" and Wickham Soap Co. "1912 Irish Fern". Easy to lather, protective slickness, light pleasant scents.
Saponificio Varesino Institute Karite Pre de provence TFS Razorock. Some are vegan and some tallow. Caties bubbles
TFS soaps are very good, in my opinion. As a basic and cheap soap, I like Klar Kabinett as well. Slick lather, very middle of the road scent, not as good as TFS regarding post shave feel for me.
Sudsy Soapery soaps are awfully hard to beat in my opinion for simply superior performance. Factor in the relatively low cost (~$2/oz) when you catch it on sale, and it becomes a great value as well.
Yes, I know. It was a joke, being that tallow is made from beef (or sheep) fat, and both animals are herbivores. On topic, TSD and Crowne & Crane make some excellent vegetable based soap.
There are a lot of good ones these days, but as far as "the best," I would have to say... Martin de candre Saponificio varesino Catie's bubbles