The benefit is definitely not having to drag your bags. Of course, some would rather do that than trusting the airline to take the bags
The long delayed Airport Express is now expected to open from Taipei Downtown to TPE the end of 2015 (that is not a typo, next year)! It is crazy how long it has taken.
Then...it is expected to be a 35 minute trip on the most direct train (that makes the least number of stops). Now you can take the bus in about an hour and it gets you to various parts of Taipei. So, I wonder how much gain there is really going to be for many.