AngularJS offers a robust solution for developing cross-browser compatible web applications, addressing the challenges posed by browser diversity and JavaScript intricacies. The framework's recent versions, particularly Angular 6, are designed to be lighter, faster, and more user-friendly, supporting progressive web-app development with features like offline experience and push notifications. Despite its strengths, Angular faces compatibility issues with certain browser versions, such as Internet Explorer 8, and requires specific coding practices to overcome challenges like CSS rendering and script-related issues. Developers are advised to use prefixes for new CSS functionalities and dynamic loading of JavaScript files to ensure compatibility across different browsers. Thorough unit testing across various devices and browsers is essential to guarantee optimal performance, and platforms like LambdaTest can assist in this process. The importance of cross-browser applications lies in their ability to provide consistent user experiences, reducing support tickets and allowing developers to focus on enhancing their websites.