"Jiggs is so broken, all she has to do is press downB to win."
- Wife
But yeah, I have a mild amount of experience against a Jiggs of questionable skill (He plays Jiggs about as well as I play Ganon) so I guess I can say a couple things on the matchup.
Dedede can get out of the WoP with his UpB's super armor if he times it right, but a good Jiggs player can probably time it so Dedede won't have time to do so.
I have a hard time grabbing Jiggs because she's in the air so much and basically spends most of her time poking me with bair and such. On top of that she's so floaty that often times I won't be able to techchase her since she'll just jump out of it lol (but it's ok because fresh bthrow does 16-17% which is like 1/5 of the amount needed to kill Jiggs with utilt). Jiggs has a ton of range on her aerials which when combined with her air speed makes her even harder to grab than Wario sometimes. I'm not sure whose aerials beat whose but I think our bair has more priority than Jiggs' aerials. If Jiggs gets us in the air she can juggle us pretty well with uairs for some good damage but she doesn't really have anything to follow them up with that I know of (rest maybe? lol).
Rest is actually pretty bad on Dedede since it doesn't really kill him until >100%. At the same time though I can't think of any better kill moves lol. Another important thing to note (and I know this goes without saying for Jiggs but it's especially important here) is that if you miss a rest, Dedede will charge an Fsmash which, if it gets charged fully, can kill Mario at 17% (This means that Jiggs can be killed at like, idk, 10% or less). In fact, because Dedede is so heavy and powerful, if you don't kill him with rest you'll likely lose a stock.
As far as stages go, Jiggs wants to avoid ceilings with low stages like Halberd and take Dedede to places with plenty of platforms like Battlefield, Brinstar, and Norfair (if it's legal) or places with big ceilings like Jungle Japes (I think Pictochat has a big ceiling too? idk).
This matchup is really close, and it's hilarious how Dedede is considered a counter for Snake but dies to this little puffball.
I'd say 55:45 Dedede from personal experience.