I think it is fair to point out that *all* animal fat or tallow based soaps produce glycerine during the saponification process. Whether that glycerine is retained in the soap or separated out (and used for the manufacture of old-school dynamite) is up to the manufacturer. Vegetable oil soaps typically do not contain much in the way of triglyerides, therefore do not produce appreciable amounts of glycerine when saponified, so if it is desired in the final product, must be added in.

A formulated soap's ability to create lather will be dependent upon the type of soap ingredients used, other adjuncts (lanolin, glycerine, fragrances, etc) and the hardness of your water. Hard water means less prominent lather.

Not all opaque (non-clear) soaps have "dyes" (really, these are pigments, not dyes) to make them opaque. Most fat based soaps are opaque naturally, and tend to be hard. Vegetable oil soaps are more likely to be clear, and tend to be soft.

Clear glycerine soaps *can* produce a rich lather, but are more sensitive to water quality (hardness) than a properly blended soap. Transparent glycerine soaps typically don't produce as good a "glide" as properly blended soaps, either.

In the end, it's all about the formulation of the soap & how it works on *your* skin. Find several that work well, and stick by them. I'm always on the lookout for new/better soaps, but always have my stand-bys.