The difference is sometimes huge. For instance, 人間的な can have a nuance of "humane/humanitarian", so 人間的な行動 means "sympathetic/moral/ethic action". On the other hand, 人間の行動 is just "action of people/human-being". Similarly, 文化的な and 経済的な can mean "civilized" and "reasonable/economically efficient", respectively, which 文化の and 経済の don't have.
You can see the difference in meaning in the example sentences in dictionaries or the real usages you'll come across. Concrete examples are often helpful for understanding rather than a comprehensive explanation.