At their core most console RPGs strive to simulate the experience of the tabletop though most seem to fail in replicating some of the more interesting aspects of pen and paper gaming.
1. Setting and Genre: The videogame RPG genre is dominated by fantasy (mostly Tolkienian from Western developers). I'm not saying that there aren't exceptions, and some those exceptions aren't amazing, but I can walk into my FLGS and find six flavours of cyber-punk, a metric cart-load of science fiction, westerns, espionage, Hong Kong action movies, anything else you'd care to name or at least a setting-less system that can accommodate my bizarre whims (GURPS Jane Austen). A similar look at my unfriendly corporate-run videogame store and find a few thousand fantasy titles and a handful of sci-fi on the racks.
2. Scope and Scale: Anyone else tired of crossing the land of Far-Far-Away to defeat the evil arch-wizard Badguy? It is possible to make a rich and interesting game within a single location, the last two Persona games come to mind. Saving nations as an end goal is as tired as saving the world, which is as tired as saving galaxies, and the novelty of conquering any of those places is starting to wear thin, too. You can create an engaging and compelling plot with the world at stake, and in an eight year career of table-top gaming I have saved the world once, and had one group I GM-ed save a city. Also legend tells of a con game of GURPS where the players did nothing for four hours except go roleplay a picnic. Not that I want a Final Fantasy: Picnic Chronicles, but my point is that there's unexplored options.
3. Choices that Matter and True Non-linearity: Most Western RPGs have gotten big on boasting a complex system of choices and multiple endings based on those. Except they really don't. Some cutscenes get changes, some dialogue options get altered, but you're still hitting the same plot points and set pieces and sure your ending cinematic might be different but the final fight is still the same. These games also claim to offer open world gameplay, and you certainly can shuffle around the plot points and side-quests, but can't truly go off the rails. Contrast a well-run tabletop game where even the GM's initial plan is about crossing distant lands (with silly names) and defeating Evil Wizards (also with silly names) and the players suddenly decide its far more interesting to clean the thieves guild out of the slums where their uncle lives and a GM can roll with that and everyone gets to have fun. Oblivion actually shines in this respect because the second you get out of prison you're allowed to ignore the main plot in favor of well almost anything you feel like in that game.
4. Urgency: Ever notice that the best time to get all the ultimate weapons and finish up those last dangling side-plots is about thirty minutes before the meteor crashes into the earth killing everyone while the bad guy laughs? Yeah, this annoys me, it breaks any suspension of disbelief I once had in the game. Any GM who catches his players selectively inbreeding giant chickens during the climax of the game will let the world end, tell his players its their fault and laugh at them for their failure. The last two Persona titles (especially 4) are great at giving you very hard deadlines to complete each major plot point without completely railroading the player.
5. More ways to Solve a Single Problem: Across every RPG ever made there is a locks that can't be opened without specific keys, walls that can't be climbed, chasms that can't be jumped, windows that can't be opened. This is stupid, game developers: fix that. On a bigger scale this prevents some of the great stories you get out of a table-top game when you MacGuyver a few feather tokens, a gust of wind spell, and a small rowboat to save the day. Game developers, you give me an airship but you won't let me use it to ram the dragon on top of the mountain, why not?
6. Social Interaction: MMOs already manage this really well, but one of my big draws to my weekly game is sitting around with some friends and just having fun geeking out. More console RPGs need co-op play, and for me, the best part of my Eternal Sonata experience had little to do with the game but playing the last four hours of the game with a friend of mine on a second controller.
I'm not trying to say that either tabletop or computer is better than the other, only that if the goal of an RPG development team truly is to bring the experience of a pen and paper game to a home console, then there a number of aspects of the former that have been neglected in the latter and that adapting more of the ideas present in pen and paper games will make for better video games, and more fun for us all.