SamIAm makes a lot of great points. I would only add that not only did Hudson not ever put a serious effort into making top-quality CD platformers, they moved their platformers over to the Super Nintendo mid-generation, and kept releasing major platformers on the NES during the TG16's life too. Of course they were doing the same with other genres, but this is more noticeable with platformers because the other genres Hudson focused on were better-covered on the TG16 and CD, including shmups, RPGs, digital comics, and the like.
But platformers? Hudson's only HuCard platformers during the '91 to '95 period after the SNES release are Jackie Chan, Doraemon Nobita no Dorabian Nights, and Bonk's Revenge in '91, New Adventure Island in '92, and Bonk 3 in '93. They did not make up for that dropoff after '91 with CD titles, as Hudson's only Turbo CD platformers are Bonk 3 CD, Doraemon Nobita no Dorabian Nights, and their only CD-exclusive platformer, the pitifully easy and dated Bakushou Yoshimoto Shingeki (it's kind of fun, but short, easy, and looks dated.). Doraemon is from '92, the other two from '94. They released no platformers on the system in '95, though they did release one side-scrolling beat 'em up with a few platformer elements on the next-gen PC-FX that year, Zenki FX.
If we add in sidescrolling action-RPGs with some platformer elements, you can also add one HuCard game, '91's Dragon's Curse (port of Monster World 2); and three Turbo CD games, from '91 Ys III, and from '94 The Dynastic Hero (port of Monster World 3) and Blood Gear.
Meanwhile, between '91 and '96 Hudson released Adventure Island II, Adventure Island III, Adventure Island IV, Felix the Cat, Jackie Chan, Beauty and the Beast (Western-developed), and Bonk's Adventure on the NES; Bonk's Adventure (semi-original, not a port), Bonk's Revenge on the Game Boy (original title, not a port), Adventure Island (remake of Adventure Island II), and Adventure Island II (remake of Adventure Island III), Felix the Cat, and Milon's Secret Castle (remake, not port, of the NES game) on the Game Boy; and Super Adventure Island, Super Adventure Island II, Super Bonk, Super Bonk 2, Hagane, Disney's Beauty and the Beast (Western-developed game), An American Tail: Fievel Goes West, Inspector Gadget, Zenki: Rettou Raiden, Zenki: Denei Raibu, and DoReMe Fantasy (Milon 2) on the SNES. The NES games released between '91 and '94, the GB ones between '91 and '94, and the SNES ones between '92 and '96 (only DoReMi Fantasy is from '96). Oh, in '97 Hudson released one more GB platformer, Bomberman Pocket, but by that point the TG16 was essentially dead.
Hudson clearly just decided after the release of the SNES that since there were more platformer fans on Nintendo's consoles, they would release most of their platformers there. Hudson never was able to match Nintendo or Sega in quality that generation either, at least in my opinion -- Bonk's good, but not quite Sonic or Mario World great -- but they definitely don't seem to have tried very hard to get platformer fans to stay on their system after 1990, not with how they released so many more platformers for Nintendo's consoles between '91 and '95 than they did their own.
This wasn't always true, though-- if we go to '87 to '90, when the PCE was doing well in Japan, they did not release even one standard platformer for the NES, even though they were still releasing a game for it here and there. The only release for the Famicom during that period that was even partially a platformer is Xexyz (it's part platform-action and part shmup). Meanwhile, on the TG16/PCE during this period: JJ & Jeff, Bikkuriman World (platformer action-RPG), Keith Courage, Aoi Blink, Momotarou Katsugeki, and Bonk's Adventure; on SuperGrafx: Madouou Granzort; and on Turbo CD: Monster Lair (platformer/shmup). Not a lot of games, but again, they had even fewer on Nintendo during that period, only one and it's just part platformer.
Earlier on Hudson had released a bunch of NES/FC platformers. Between '84 and '87, Hudson released Nuts & Milk (puzzle/platformer), Lode Runner (Western game they ported to the NES), Championship Lode Runner (sequel to that game), Challenger (only partially a platformer), Adventure Island (port of Wonder Boy), Mickey Mousecapade, Milon's Secret Castle, and Ninja Hattori-kun and Takahashi Meijin no Bug-tte Honey (only partially a platformer). But no more after that until '91's Jackie Chan unless you count Xexyz.
As for NEC, the other first party, they didn't help matters, because NEC in Japan released few platformers of any type. On HuCard, released between '89 and '91: Genji Tsushin Agedama, Son Son II (by Capcom), Tiger Road (port of a Capcom game), Altered Beast (sidescrolling beat 'em up, port of a Sega game); on SuperGrafx ('90): Ghouls 'n Ghosts (port of a Capcom game); on CD (one in '89, the rest in '92-'94): Horror Story (autoscrolling run & gun game maybe you could call an "action-platformer" of sorts), Altered Beast (sidescrolling beat 'em up, port of a Sega game, and that one title from '89), Bonanza Bros. (port of a Sega game), Chiki Chiki Boys (another port of a Capcom game), and Strider Hiryu (another port of a Sega game). Also add Renny Blaster and Mad Stalker (from '94-'95) if you want to count that sidescrolling beat 'em up, but it probably shouldn't. Bazaru de Gozaru No Game Degozaru from '96 is also worth mentioning, but while it has a side view, the actual gameplay is purely a puzzle game, not a platformer. Overall it's a thin library made up of mostly ports, there. Son Son II is great, but it's from '89. After Mario World and Sonic's releases, about all you have are a few old ports, run & guns, and beat 'em ups. Some of them are good games, sure, but it's not many games total, and third parties were most definitely not making up the slack.
In the US NEC did publish some, of course, but they weren't exactly Mario or Sonic quality... :p (Night Creatures, Ghost Manor, TailSpin, Darkwing Duck, Impossamole on HuCard; Addams Family, Camp California on CD...)