Eva is a better experience on board. Their B787 fleet is modern and good. If Eva is cheaper by 1200, I will take Eva.
CX is good but their lounge is also very crowded. But AA has a good lounge in DFW. Not sure about lounge access for BR.
if you wanna visit Taipei, a great city, then take Eva! I generally find EVA to be better than CX but their B773 fleet is quited dated and narrow. B787 seats are better.