Good question. Make an alt, friend yourself, and find out, then tell us about it. My educated guess is that the priority will be the same as the eidolon list (inventory) sorted by level (or one of the other sorting options that gives approximately the same result as sorting by level, like total power). The easiest way to test this hypothesis would be to compare 6 different LV1 eidolons of the same element and see which appears in the friend eidolon list, then remove those eidolon one-by-one. Might want to do it inbetween events so friends don't get mad.