Jigglypuff is ranked 36th out of 41 on the official tier list, in the midst of the D tier. This is an improvement over its Brawl placement, where it was 36th out of 38, but still a very significant drop from its Melee placement of 3rd out of 26.
Seeing as how Jigglypuff was one of the worst characters in Brawl, it has been nearly fully returned to its Melee incarnation for its appearance in Project M. However, Jigglypuff's tournament success relative to the cast is still reminiscent of its significantly less viable Brawl appearance. Jigglypuff still boasts good matchups in theory against Melee's top tiers, such as Falco, Sheik, and Peach; however, the revamped Melee mid- and low-tiered characters and Brawl newcomers give it significant trouble. Many of them now have better disjoints, projectiles, and KO confirms, which makes it much harder and riskier for Jigglypuff to drift around opponents and intrude into their space as it could in Melee. Additionally, Project M's frame leniency for advanced techniques arguably benefits Jigglypuff the least out of all the returning Melee characters, as it was already not a technically demanding character. This drastically reduces Jigglypuff's consistency in tournament play, since more technically demanding characters such as Fox will now make fewer mistakes that it can capitalize off of.
Jigglypuff is also held back by the new stage list. Project M introduces small, cramped tournament legal stages such as the revamped Green Hill Zone and Wario Land, which are huge detriments to Jigglypuff's survivability. Jigglypuff also still has problems fighting on Final Destination, and the low ceiling on the now-starter Pokémon Stadium 2 can work against it as well. With the increased number of stages, tournaments often allow two bans even in best of 5 sets, which means that Jigglypuff's opponents can ban its best stage in Melee, Dream Land, while the Jigglypuff player cannot ban all of its bad stages at the same time.
Overall, while Jigglypuff can still be a capable character in Project M, it is often considered bottom tier by the competitive community due to its difficulty in adapting to the new characters and stages.
Changes from Melee to PM
Jigglypuff has remained relatively unchanged from Melee to Project M, although it has gained a few additional options from Brawl-based mechanics.
Changes from PM to P+
Up to date as of version 3.6.
In competitive play
In versions after 3.0, Jigglypuff got back its yellow crown costume from Melee. It also received a new costume that gives it a more opaque color and fairy wings, which emit sparkles when moving in midair; this heavily references Jigglypuff's change to being a part Fairy type in recent Pokémon games (more specifically the Generation VI games), which is a newly-introduced elemental type.
PMDT had confirmed on their subreddit that Jigglypuff would have an additional alternate costume based off its headband costume in Melee in a future version of Project M. While it never made it into the mod officially, it was later released on the Brawl Vault.
After it could not appear in Project M, Project+ brings new costumes for Jigglypuff, including the previously unused headband costume.
Z-Secret Costume: Luchador Mask (El Globo)
R-Secret Costume: Giant Bell Jigglypuff from "Fierce Battle! Ancient Pokémon" (Pokémon Anime)