Free or Fee Products and Services
Question: "From a product management point of view, should free services be planned and marketed differently than paid ones?"
From a product management perspective the planning of a product and its marketing, regardless of if this product is provided for free or for a fee, should be done similarly and according to the same product management methodology.
The general notion is that all products and services are essentially a solution to a market problem. The objective of product management is to plan a product that provides the required amount of functionality and proper value that the market needs. Making money or losing money is actually a by-product in the process of solving the market problem.
Question: "Let's assume a free web-based feature to an existing web product. If some of the users are totally unhappy with the new feature while others feel content, will that be considered good product management?"
This depends on the proportion of pleased and displeased users. All products are built for a "Persona Set" which is the collection of all the personas selected as representative users of the product. A product and the bulk of its features are always designed primarily for the dominant persona in the persona set.