Taipei is one of my favorite Asia stop-overs but that is because of family and friends. For sight-seeing, there's the Palace Museum; other sights pale in comparison to what one can see in Beijing.
First timer - Beijing hands downs! Shoot over to the China sub-forum to see what you can do in two days (you can spend 5 days and still wish for more time). Or send me pm.
September is also still hot and humid in Tapei. Beijing weather starts to turn around September - can be warm, can start to cool down.