Discovering the Python library difflib can significantly streamline and enhance the process of comparing text data, as exemplified by Julian's experience in comparing two to-do lists. Initially, Julian's approach involved manually checking each item in the lists using a loop and conditional statements, which quickly became unwieldy and insufficient for identifying differences. The difflib library, particularly its Differ() class, offers a more efficient solution, allowing for detailed and readable comparisons by highlighting differences with specific markers. This functionality mirrors the Linux/Unix diff command, providing a familiar interface for users. Julian notes that difflib is part of the broader Python standard library and can be transformative for coding practices, as demonstrated by its application in various projects beyond simple text comparisons.