If Horatio Gates had caught a bullet at some point during the Saratoga Campaign and Arnold was correctly credited for the most important victory of the war to that point, Arnold, not Gates (for the obvious reasons) gets sent south (after recouperating from his injury- he caught a musket ball in his ankle, shattering it.) and, with Daniel Morgan as his second in command.
Arnold was probably the best field commander the Continental Army had, and Morgan (as he would show at Cowpens OTL) was probably a close second.
Expect a far different southern theater with Arnold in command, as Arnold probably wouldn't have let Lincoln get trapped in Charleston.
Perhaps Lincoln would have had to concede the city regardless, but I doubt Arnold would have left him (and his 5,000 troops) to be trapped and captured when the city fell as Gates's inaction did.
Take Monck's Corner, for example. Morgan would defeat Tarelton OTL at Cowpens. He may very well defeat Tarelton here, allowing an avenue of escape for Lincoln and his men. Same could be said at Lenud's Ferry. If Tarelton's defeated at either or both of these engagements, (and Morgan's cunning at Cowpens says he could very well have done so) Lincoln and most of his men could probably escape to fight another day.
What then, would a southern theater with Arnold in command and a sizable force with which to fight Cornwalis look like?
Depends on what Arnold would have done. Ultimately, Nathanael Greene's default strategy of rapid withdrawal, forcing an equally rapid advance by Cornwalis, which, in turn, caused Carnwalis to outstrip his overland supply lines, forcing him to remain by the coast to resupply by sea, which ultimately put Cornwalis on a tiny peninsula between the James and York Rivers...
Perhaps Arnold takes the same approach despite having a larger force at his disposal, and, rather than inflicting a Pyrrhic victory on Cornwalis at Guilford Courthouse, Arnold (with the ever present Morgan at his side) decisively defeats Cornwalis there.
Thing about Arnold though, was that he was only a defensive general when he had to be (read: when he was significantly under-manned), and with such a large force directly under his command in the south he'd probably be more inclined to his instincts, that of an offensive general.
It's not out of the question that he may have taken some very important insight about fighting a defensive campaign away from Saratoga. Thus, at Guilford Courthouse as a "Saratoga of The South" isn't entirely out of the question.
One thing's for sure, it'd make an oft forgotten theater of the American Revolution unforgettable.