This is the most common confusion in the category, and the two products are not substitutes for each other.
A softener removes calcium and magnesium by ion exchange. It stops scale. It does nothing about chlorine, taste, smell or disinfection byproducts.
A filter, carbon, at the point of entry, reduces chlorine, the trihalomethanes chlorination leaves behind, and taste and odour. It does nothing about hardness.
For most homes on city water in this metro, the filter is the one that matters and the softener is the one being oversold. For most wells, you want both.
What we install, and what it costs
Softening is part of both standard rates: the city water system at $2,900 installed and the well water system at $4,500 installed. If your test says you do not need the softening component, that is quoted separately and comes in under the standard rate. The standard is a ceiling for a typical house, not a starting point.