Well, the Bonsai West soil is cheaper
, but don't forget to add in shipping. A fifteen lb bag is going to cost ya...
The difference here --I think--is that Bonsai West is an actual bonsai nursery and probably makes its own soil. Bonsai Outlet doesn't have the nursery facilities and probably buys its soil elsewhere.
All this is speculation on my part. I've not bought anything from either place, but I have seen Bonsai West as a vendor for many years. They're a known quantity.
The differences in sourcing, ingredients and composition of soils are endless. Some fly-by-night-vendors sell crappy soil for a lot of money (neither of these is one of those). Beginners are often bewildered by making or buying soil. Bonsai soil is the basic building block for success. Scrimping on it, using the wrong stuff, using commercially made stuff that doesn't live up to its billing will kill your tree.
That's why it is so important to contact your LOCAL bonsai club. Its members have all been through what you're going through. They know what works in your area, where to get decent soil--or, most proably, make their own which you can buy (or receive free if you have generous club members) from them.