Now I really didn't want to reply to this thread as it usually opens a can of worms...but comments like "some of the best soaps on the market" make me REALLY nervous.
What I am about to write is not based on any scientific research - but only on personal observation over the years:
I think, that saponified tallow (ie tallow that has been reacted with a base such as Sodium or Potassium Hydroxide) helps to stabilise the water in your lather.
What does this mean for you: Lather with a high water content usually means better glide - while lather with a high air content means the opposite. Those tiny and large air bubbles pop and stop your razor. Water and soap on the other hand produce a tiny film, that makes your razor glide better over your face.
In my experience non-animal fat soaps often cannot take that much water - ie the lather collapses, when you add more water. While this might not be a big issues for the glide, you loose the protection or cushion of the lather - the 2nd most important property of a good shaving lather.
Tallow (and other animal fats) somehow stabilise the water content in your lather - enhancing the glide without loosing the protective properties.
Now this is of course only true for a well formulated soap. Many soap makers add tallow/animal fat just to have it on the label, but the content is too low/wrong and you do not get the desired benefits. The main content of these soaps (stearic acid) is much cheaper than tallow
Similarly other soap makers try to emulate tallow properties by mixing other (non animal) fats into the soap.
HOWEVER: tallow is still A LOT cheaper in comparison to exotic fats like shea butter.
What is the bottom line: Without fantastic lather, there is no good shave and tallow soaps are in my experience still the cheapest ones producing fantastic lather.
If you eat animal meat - tallow soap IMO is a fantastic product, so that less of the animal goes to waste. As are secondary cuts, bones for broth, leather products...we want to use as much of the animal as possible, don't we?
If you are vegetarian/vegan: as long as others eat meat - you do the world a service by using their waste product (tallow) for your soap - no palm tree plantations, less chemical plants for stearic acid production...
If you are 100% opposed to using animal products: please think, before falling for lines like: now with shea butter. Do a quick research and you will find, that if any one wants to use shea butter INSTEAD of tallow, the soap would most likely cost 50$ or more a puck. The addition of 0.5% shea butter to a soap does not substitute for the lack of tallow.
There are some decent vegetarian soaps out there...but you are missing out on some of the REAL best soaps on the market