This was inspired by [link] which compares DuckTales with Darkwing Duck. However, it's not much of an "old vs new" since DuckTales only came out around 5 or so years before Darkwing Duck did. So here's a REAL Old vs. New...the original Uncle Scrooge comics (the very basis of DuckTales!) versus the show itself.

Round 1: Content
The Uncle Scrooge comic was the work of many great men, but the best Scrooge stories were done by Carl Barks (Scrooge's creator) and his spiritual successor Don Rosa (whose adventures of the Ducks continue to this very day.) Many DuckTales episodes were based on the comics (the Terry Fermies, the Golden Fleece, the marbles that had to be delivered, the lemming and the locket, etc. etc.) There were many stories that would've made great episodes, like the 24 Karat Moon, The Seven Cities of Cibola or The Prize of Pizarro, but a lot of them would've been (1) dated, (2) contained non-PC elements, (3) wouldn't have been suitable for an audience of mostly children, or (4) didn't involve any of the stock villains.
DuckTales's contemporary setting also lends itself to a lot of great original stories and characters (the episode with Gyro's vanishing ray, time travel into Ancient Greece and even further behind that, a genie, etc.) It also had some pretty good feature-length multipart stories (something that's hardly ever done in Uncle Scrooge comics.)
WINNER: Original Scrooge, mostly for the fact that some of my favorite stories never made it to DuckTales.

Round 2: Uncle Scrooge
Barks and Rosa portrayed Scrooge as the classic miserly tightwad (he likes to mooch off Donald and the nephews) with a wild streak for adventure. DuckTales made him a little bit more compassionate (after all, he is a caretaker of 3 ten-year-olds) towards his family, but with that same stubborn miserly streak.
WINNER: Original Scrooge

Round 3: Huey, Dewey & Louie
The original Scrooge comics portrayed the nephews as if they were exact clones of each other (they even finished each others sentences and talked in unison.) DuckTales gave each of them a little bit more of a personality, and often involved a single nephew in an adventure rather than the set. If one thing can be said about DuckTales's portrayal of the nephews, THEIR CLOTHES ARE FINALLY CONSISTENT. Practically every single piece of promotional merchandise that was released before the DuckTales era has them wearing different colors (or even black shirts and no hats!) To this day, every kid knows that Huey=Red, Dewey=Blue and Louie=Green.
WINNER: DuckTales.

Round 4: Donald Duck
The show decided to write off Donald Duck, saying he had enlisted in the Navy and left HDL in the care of Scrooge. As a result, he doesn't have a whole lot of screen time (just a few cameo episodes.) However, in the comics, Donald has MUCH more of a leading role!
Winner: Original Scrooge

Round 5: The Beagle Boys
Why did they have numbers? Are they clones of each other? What gives? DuckTales introduced individual characters with ACTUAL PERSONALITIES. And who can forget Ma Beagle? (June Foray FTW.)
Winner: DuckTales

Round 6: Flintheart Glomgold
Barks originally had Glomgold as an Afrikaner who lived in a Money Bin with a Pound Sterling symbol instead of a dollar sign, while DuckTales portrayed Flintheart as a Scotsman that lived in a GNARLY EVIL LOOKING HOUSE. They were pretty much the same personality-wise, though.
Winner: A tie!

Round 7: Magica DeSpell
One of my favorite villains EVER, and once again, June Foray FTW. Magica's trademark in the comics were her "FOOF" bombs, and her magic was more mad science based and involved various strange ingredients stirred together in her cauldron. DuckTales has her spells in rhyming couplets, and Mt. Vesuvius is now a carving of her HEAD. She's a lot less dangerous than she is in the comics, though.
Winner: Original Scrooge

Round 8: Supporting Cast
Recurring characters in Classic Scrooge: Gyro Gearloose, Grandma Duck, Daisy Duck, Mrs. Quackfaster (the secretary,) Gus Goose...not very many other than the villains, I'm afraid.
Recurring characters in DuckTales: Mrs. Beakley, Webby, Doofus, Launchpad McQuack, Gyro Gearloose, Ducksworth, Fenton/Gizmoduck, Fenton's mom, Bubba, etc. Lots of new people, lots of different personalities, some good characters (Gyro Gearloose), some bad characters (Bubba, Doofus), some so awesome they had to be reused in another show (Launchpad).
Winner: DuckTales

FINAL SCORE:
Original Scrooge: 4
DuckTales: 3
Tie: 1

The original Scrooge stories just squeak by~ IMHO, you can't improve on an original, but you CAN build on it enough to make something with a new, distinct style but with the same flavor as the original.

Postscript: I'm now wondering what the hell kind of relationship Doofus and Launchpad have seeing as there was one episode where they were eating breakfast together in bathrobes.