As it has been noted several times already, it depends on the genre of the game in question; some games are frustrating to try on a console, and vice versa.
As a general rule, controllers lend themselves to games where you can expect a lot of action and are in control of only a single character. A controler's simple layout lends itself well to context-sensitive actions and "touchy-feely" gameplay; it's just easier to do things like "a little more" and "a little less" on a controller. All aspects of gameplay simply have to be more elegant when you use a controller, leading to a great deal of streamlining; however, this is also what makes a lot of games very fun to play at the same time.
Where the keyboard & mouse excel is at providing a wide set of options and precision. Action does not need to be fast-paced, but there's also very little preventing games from being very fast at the same time. Anyhow, precision and options are still the main focus. One button press (or mouse click), one action; and a button for every individual action.
Neither style of gameplay is inherently better than the other, they're simply different styles which lend themselves to different types of gameplay. People need to realize that just because you prefer one of these styles does not mean that it is better than the other.
---
To compare the different styles of gameplay, there's two genres I'll take a quick look at: FPS games and RPGs, both of which are available on both PCs and consoles.
FPS games were predominantly on the PC until the last decade (and a half?) or so, and for a good reason: the mouse allowed for faster and more precise aiming. Throw in the keyboard allowing players to quickly switch between a dozen weapons very quickly, and it was a natural fit for the keyboard & mouse setup. Halo: Combat Evolved is usually credited for being the game which made FPS games much more viable on the consoles, and there's a few very simple and elegant changes to the genre it made which made it work: only allowing you to carry two weapons at a time (no need for fancy menus to select the weapon you need), grenades and melee attacks being baseline abilities and independent of the weapon you're using, slowing down the player's runspeed to a more managable pace (... I think), and the easy-to-read shields & health meters (rather than a numerical readings). The regenerating shields are also an elegant change to the genre, though that particular change probably wasn't necessary to make the move to consoles (though it probably helped). Anyhow, these changes made FPS games fun to play on consoles.
For RPGs, its easier to look at the older Final Fantasy games; specifically, the Active-Time-Battle (ATB) system. This move away from the older turn-based approach (everyone gets one action per turn), it allowed for players to include a sense of speed in the games and allow everything onscreen to act in a vaguely real-time setting. But rather than issuing or queuing up commands all at once, the player takes control of one character at a time and issues the action when they need to do it (when the ATB guage/timer fills up). A PC RPG like Dragon Age: Origins (and presumably Baldur's Gate, to which DA:O is considered a spiritual successor) takes the "pause-and-play" approach, where commands are issued or queued up for the whole party in advance then executed in real-time. The former is more simple & elegant, the latter allows for more complex actions.
In both cases, consoles have to take an elegant & streamlined approach to accomplish what a PC does. It may have to sacrifice complexity to allow for quality gameplay, but at the same time it is more accessible. Again, neither is fundamentally better; they are merely different styles.