For starters, John Andre probably survives the Revolutionary War.
And while Arnold's victories would probably be forgotten in his own day, if he never turns traitor, then American posterity will probably eventually remember him as one of the Revolution's best soldiers and he will have numerous monuments/memorials across the US - compared to OTL where his name is a byword for traitor.
If he's in overall command at Saratoga, he'll get the credit for bagging an entire British army in the field, something nobody would overlook in his own time. There were elements of Congress that wanted to replace Washington as CinC of the Continental Army with Gates after Saratoga, and Gates (who'd deluded himself into thinking he actually was responsible for the victory, not Arnold) was all for it. Mainly because he hated Washington and had an ego that made Arnold look meek by comparison.
Arnold, on the other hand, greatly respected Washington (at least, at that point) and wouldn't have presumed to replace Washington, even with such a victory to his own credit.
As such, I think, if Arnold is in overall command at Saratoga and gets his due credit for the victory, he probably heads south, to Valley Forge, and becomes Washington's right hand.
The following spring, when Washington rolls out to face Clinton at Monmouth, he sends Arnold to lead the attack and you have a much different Battle of Monmouth, as Arnold was no Charles Lee- Arnold wouldn't have dragged his feet getting to Monmouth Courthouse and would have launched his attack on time, per Washington's plan, and then...butterflies.
Biggest butterfly off of Arnold leading the attack at Monmouth, Arnold would have attacked and pressed the attack, unlike Lee who dragged his feet getting to the objective, then disengaged and retreated shortly after first contact with the opposing force.
If Washington still uses the same general plan for Monmouth as OTL (difference being Arnold leading the advance force and attack), you get a much different outcome, as Washington isn't forced to alter the battle plan upon arrival with the main body of the Continental Army, as he's arriving with his lead element engaged with the enemy under Arnold, rather than fleeing the field, as they were under Lee.
Where it goes from there is good food for thought, but if Monmouth is a clear cut Continental Army victory, rather than a morale boosting draw (which it was OTL), Arnold probably ends up being sent south to counter the British in 1779.
While Arnold isn't going to 'drive the British back into the sea', I think he could have facilitated an escape for Lincoln's forces at Charleston, then waged a more effective campaign against the British in South Carolina than Gates did...but then, all he has to do to accomplish that is not abandon his own army in the field at Camden, and that's only if Arnold also decides to give battle at Camden, as Gates did.
Who knows? If Arnold can help facilitate a successful evacuation of Lincoln (and his 4,000 CA regulars) from Charleston (or even just half of them), the CA position in the south is radically altered from OTL. Arnold might choose a better spot than Camden to engage Cornwallis, and either stalemate him or possibly defeat him.
The nature of that defeat would depend on what Arnold's plan is, but I think he adopts a strategy of forcing Cornwallis to pursue him inland and away from the coast before giving battle.
The last remaining question after that is whether Arnold goes for one decisive battle against Cornwallis immediately, or chooses a series of small battles, along a pre-planned course of retreat that wears Cornwallis and his army down slowly before going for the decisive battle at a per-determined spot at the end of that route of retreat.
Washington would still end up Father of His Country; the man had the temperament and thick skin the leaders of the Constitutional Convention were looking for (and desperately needed) for the first President, but Arnold may end up with a cabinet seat (Secretary of War, perhaps?).