Naruto would become more self - reliant. Without the support system of the village, he'd have to figure out how to survive on his own. This would make him tougher both physically and mentally.
Naruto's character would mature. He'd no longer be the naive boy from the village. The street life would force him to grow up fast. He'd have to make difficult decisions, like whether to steal to survive or rely on his wits. His relationships with others would also change. Instead of the usual bonds in the village, he'd form more tenuous, but in some ways more profound relationships with the street - dwellers. His understanding of power would shift too. It wouldn't just be about being a strong ninja in the village, but about having the power to change the lives of those on the street.