Largely because of the presence of slavery, few immigrants came to the South. It's not like southern landowners really had a choice which method to use. Nobody wanted to compete with slave labor, a major factor behind northern opposition to slavery and its spread.
There is considerable evidence that plantation slavery, on a well-run large plantation, was more "economically efficient" than free labor. One source I ran across claimed that plantations were about 40% more efficient on average than northern family farms, and about 60% more efficient than southern family farms.
This is, of course, the efficiency for that particular organization. It seems pretty clear that it was not an economically beneficial system for the society as a whole. Just as illegal immigrant labor today can be highly profitable for a restaurant or lawn service, while having detrimental side effects that the whole society pays for.
No less a figure than Tom Jefferson sought European immigrants for Virginia. But in his day, the few European rulers he negotiated with were willing to let their people go.