Dan started the year as Scotland's first-choice fly-half but lost his place to Gordon Ross.
The Glasgow Warriors player came back into the side against Romania in the summer when the Leeds Tykes player was injured.
Ross was not included in Hadden's squad for the visit of the Pumas and, despite Dan's recent goalkicking woes in the Heineken Cup tie against Leinster, a week after a man-of-the-match performance against Bourgoin, the Australian-born player warded off the challenge of Edinburgh's Phil Godman, who forced his way into the squad after his impressive performance against Wasps two weeks ago.
Hadden waxed lyrical about the Glasgow player, saying: "Credit to Dan because there's no doubt that Gordon Ross was my number one in May but Dan has improved a lot.
"I've watched a lot of stand-offs this year and only Dan Carter is head and shoulders above the rest.
"We expect a stand-off to be Superman and to do everything brilliantly but I've watched Jonny Wilkinson and Charlie Hodgson and they have had mixed performances.
"Dan (Parks) has had a number of outstanding games in terms of his decision-making, accuracy of his work, defensive duties and kicking.
"So in terms of the all-round package, Dan has produced a level that I hadn't expected from him this season.
"Getting that level every single week is not easy. There was a much documented incident last weekend but Dan doesn't have to do all the kicking.
"His level of communication has gone up a notch and it is significantly better than that of Gordon or Phil."
After acting as interim boss for the games against the Barbarians and Romania in the summer, Hadden is taking the Scots into his first match since being appointed permanent head coach.
The former Edinburgh Gunners chief is initially looking to rejuvenate the spirits of the Scotland players.
He said: "If you don't enjoy turning up for your work then you won't perform well.
"It's not a happy-go-lucky holiday camp type of enjoyment but it's guys looking forward to training who feel good about themselves, who look forward to playing for Scotland and particularly winning for Scotland."