Water softeners are usually used to remove minerals from water. A whole house water filtration system, however, tries to address a broader case of water quality issues. But when making a choice between water softeners and a home water filtration system, it would basically depend on the quality of water to be treated.
The most common form of water softening systems are salt-based systems that replace water minerals with salt ions. These softeners typically add sodium and potassium through a tank to soften hard water coming from the ground. Most rural and municipal systems have hard water, which is water taken from the ground or wells that are known to have high percentages of dissolved materials such as calcium and magnesium. Other forms of softening systems include the non-salt ones that target any traces of hydrogen sulfate and oil and magnetic systems that take out the metallic minerals found in water.
Whole house filtration systems often involve a two-stage system where the first stage targets particles larger in size and the second focuses on trapping smaller particles in the water. Compared to water softening systems, whole house filters trap particles larger than the membrane rating found in the second filter. Metals, non-metals and particles such as bacteria are then successfully removed. These systems will be able to reduce hard agents down to a sub-micron level similar to how a water softener would. The only difference is that in water softeners, your water would have salt in it.
The effectiveness of a filtration system would depend on how well it successfully removes particles from the water. Salt-based water softeners usually fall in the range of $400-$2,700. The price of a water filtration system can be anything between $800-6000. Naturally, the more efficiently the particles are removed, the higher the cost of the filter.
Basically, if the wanted solution is to make water less hard by removing contaminants such as heavy metals and sulfates, then a softening system will definitely be a more cost-effective solution. But if additional water quality concerns need to be addressed, a home water filtration system would be the solution a softening system cannot address.