I'm not sure what your good price on Eva is, but when my honey flew to Taipei on Eva last year, the AA ticket price was almost twice the cost of the ticket if booked through Eva's own system. As he was traveling on the office's dime on that trip, he had to forgo the AA miles (total bummer on such a long trip) and take CO miles instead. With Eva/AA, your ticket must show an AA flight number to earn the miles, or at least such was the case a year ago.