It may be like stating the obvious, but "2d" and "3d" are, of course, both 2d. The two of them appear on a flat surface. Again, stating the what we already know for the purpose of refection: the preferences people have between the two are mainly aesthetic.
Mainly, but not solely. Choices must be made about when to use 3d over 2d. Cost is one reason. 3d is becoming considerably cheaper to produce, with benefits such as reusing character models to create new animation, rather than new artwork being the needed for new animation in 2d. The ease of having a virtual camera to move freely around a seemingly 3d world makes First-Person Shooters profitable. Not to mention computer generated effects such as explosions having been studied to the point that they are practically "stock."
An almost humorously unfair comparison.
The problem is that most game companies are not taking advantage of the limitless possibilities of 3d. When a 2d character is created, it almost certainly will not be "realistic," because realism is too difficult to capture with a stylus or pencil. This is 2d's most powerful asset. Stylized characters like Mario and Sonic, even more realistic humans like those is Castlevania: SotN, are usually (keyword: usually) more appealing than the 3d dolls that are very human-like but not quite. There is something rather unsettling about a 3d model that looks human, but to our eyes, so keen to detecting human facial nuances, they are clearly foreign creatures. This contrasts to models that are quite clearly created with a unique style in mind, to tell our minds that this is fantasy. Clear examples of this are found in the Pixar film The Incredibles, or in our gaming world TF2. It is unfortunate for the gaming community as a whole that TF2 stands almost alone in this way.
Let us be fair here though. 2d can be guilty of the same awkwardness. Who remembers those old Disney classics such as Snow White and Sleeping Beauty? Who admits to sitting with their little sister, watching Don Bluth's Thumbelina on home video? Or, sat bored to death through Titan A.E.? I won't even mention Polar Express. All of these films included either rotoscoping (an animation technique in which animators trace over live-action film movement), or heavy use of live action reference to animate their 2d heroes and heroines. The result was a few characters looking eerily human, not wonderfully life-like. This seems like an oxymoron. To animate something humanly almost always results in the viewer rejecting the character's humanity. Whilst the humans who are characterized, without falling into archetypes are remembers as the most human.
2d had the luxury of being heavily populated by these stylized characters, both in design and movement. 3d on the other hand, has the curse of being almost entirely populated by anti-humans we subconsciously reject. Even great games like Gears of War almost failed in suspending senses of reality with its half-breed of the characterized and realistic models.
With all this said, if every game was stylized there would be a cry for the quasi-realistic, in all it's gracelessness. Many would probably prefer them to be a minority though, in the face of the overwhelmingly creative characters I hope are just around corner.