doing nothing through faction or through vainglory, but in lowliness of mind each counting other better than himself;

Do nothing out of selfish ambition or empty pride, but in humility consider others more important than yourselves.

nothing in rivalry or vain-glory, but in humility of mind one another counting more excellent than yourselves--

[let] nothing [be] in the spirit of strife or vain glory, but, in lowliness of mind, each esteeming the other as more excellent than themselves;