If you were to ask around, it wouldn't be hard to find practitioners of both. We call "big eye--little ewe" people self-centered or egotistical, and many of them are proud of that rap. The few who aren't proud of it wish they were more deferential to others, but they don't seem to have it in themselves.
The other extreme is the "big ewe--little eye" camp, many of whom seem to have declared themselves the world's doormat. They are an interesting group because of their varied motivations.
False humility seems benign enough. Humility under any guise is a good thing, right? Not if its root lies in the ego, and feeds on altruistic pride. One could call it a "martyr complex," where seeking the last place elevates the "humble soul" to a superior position is his own eyes.
Poor self-image is an emotional disease, often passing to successive generations in a family or community. Poor self-image is a double-edged sword, cutting toward hopelessness and depression on one side, and toward aggressive, antisocial behavior on the other. Many of these folks refuse to strive for self-improvement either because they believe they are not capable of achieving it, or because they believe they are unworthy of it, or both. And many others prey on anyone who seems to have more than they, taking their goods and mistreating them to make themselves feel superior.
Of course there's another category the title ignores, because the world's wisdom ignores them: They are the "Big God, Little I" people. They love God because He first loved them. They see themselves as God's servants, and in turn, servants of God's creation. They seek not their own glory, but do all in their power to love and glorify their beloved Lord.
They show their love by routinely giving themselves or their goods to others through acts of charity. Why? Because they fully believe their property and talents aren't their own. And their love extends even to those who mistreat them, responding with prayer and gratitude no matter what happens to them.
God's servants also love those who claim to be God's servants, but without the works to prove it. They love the pew-sitters who show up in church each week to join in the feel-good experience of worshipping God, but leave after the small talk and hand shakes to pursue their own agendas. They even love those church folks who obstruct God's work because "that's not the way we do things here."
And of course they love and subject themselves to God's undershepherds, who might put the kibosh on their ambitious plans because God's timing isn't in it. Tragically, that's the hardest kind of love to give.