First-hand experience with the 3DS Cave Story (As my first played game on the 3DS, because I'm a moron who expects some semblance of competency with console releases):
The background and foreground objects, being standard flat rectangles, were likely re-textured rather easily, and possibly by Pixel himself. As a result, aside from a few finicky 3D effects that zoom toward the camera yet go under the HUD, and the Seal Camber making the spikes on either side rather hard to see, these backgrounds are by far the most enticing part of the game. Many of them take a creative new twist (some good such as Sand Zone, and some bad such as Outer Wall and the retarded idea that the island is mostly mechanical), and are beautiful to look at.
Of course, that said, since they are the background, you aren't suppose to focus your attention on them all the time. So what of the actual characters?
Well, imagine someone put together a really good model of a character in Blender or some other 3D modeling software, but then opted to never actually texture them. Sure, the colors and general shadows are there, but the textures are just flat, lifeless colors. That's effectively every foreground object (and some background objects!) in the game.
Moreover, the game is riddled with small things that as a player you might never actually stop to appreciate, but are stupidly noticeable when done badly, such is the case with CS3DS. The teleporter doesn't flicker correctly or retain that 'upward dissolve' thing the original game had, and the player merely vanishes sloppily. The teleporter's flashy light around the player doesn't quite animate correctly either, so the player character will have already disappeared when it actually decides to turn on. Several other animations in the game simply fail to play as well, such as King attacking the Doctor with his sword, instead proceeding to face the wrong direction entirely during the brief conversation, and without his sword.
The map system, while nice in theory, is fairly ugly to look at, but is also riddled with ridiculous flaws. The design choice to highlight doors in a particular color decided it would remain consistent by every door, and as a result the clock room on the outer wall is stupidly easy to find (and in fact I don't even think that old clock block hinting it's location even exists anymore). It will also stretch ridiculously to try to compensate map sizes, causing it to ultimately look inconsistent, and not at all like an actual map system you're in possession of. It's just a window on your DS that shows the map, and no more indulgent in the fantasy than that.
The 3D the game adds, while nice to look at, also exhibits several flaws in their execution. While I said before the background was nice to look at, the camera seems to think so too and will constantly re-angle itself to show all of it. While it's used to some nice effect in the pointless additional area in 'Egg Corridor?' (whose only purpose was to use the 3D, where they could have done similarly the entire game but were too lazy to), the game is still ultimately tile-based. As a result, you'll VERY often think you're positioned in front of a common background object, for example Chaco's fireplace, but proceed to not actually examine it by pressing down until you're a smidge more to the right or left of it where the actual tile is. Instead of compensate for these obvious flaws in using 3D effects, they decided not to bother repositioning the examine boxes to be in line with the camera, rather they decided to add long streaks of light from the door to show where you're SUPPOSE to be standing. Effectively fixing the problem by calling it the player's fault, when it's clearly theirs.
Besides the 3D, even the 2D sprites you can view in 'classic' mode are flawed. Each of them now has some needless shading layer overtop of them, causing every sprite to look like a flat piece of paper dipped in ink. And you'd THINK they'd be able to actually keep the 2D animations consistant where they failed to do so with the 3D models, but you'd be wrong. Even the 2D sprites pre-programmed to work correctly in the original version for PC fail to properly animate or render. Flying Gaudi's, for example, don't flicker purple before they shoot at you. The aforementioned Sand Zone cutscene with king fails to actually have the red eyed toroko sprite.
Finally, the decided extra content in this version is... none whatsofucking ever. You don't even get a boss rush mode. All you get for beating Hell in the game is the ability to speed-run hell from the menu. Because I guess even Nicalis don't want to play the game they failed to make anymore.