Importance of UX in web applications

Websites and web applications are different in terms of audience and the purpose they serve. But with the recent rise in free/freemium model for web applications,the question of how important is UX to a web application is becoming fast becoming relevant. If you look at the web you will find websites with beautiful animations and incredibly smooth UI can be found. With the developments in front end technologies new ways are being defined to enhance user experience. So where do you think this is going? Will the web application be soon competing with these marvelous UX and UI?

Let me know you thoughts...