Short Answer: there are no casual consoles, only casual gamers

First, "Hardcore" and "Casual" are terms invented by market analysts to divide people who play games on their iPhone and Facebook-type browser games, as well as people who play non-traditional games on the Wii (Casual) from gamers who have PC, Xbox 360, or PS3 and play traditional games like Call of Duty and Madden. It's useful for identifying the two very different demographics who collectively spend an insane amount on games, but neither end of the spectrum represents true, real gamers and certainly not here.

The second divide comes from game enthusiasts on the internet who misinterpret what the divide actually means. They think it's a genre question, that shooters, racers, and sometimes RPG's (the 3 staples of the 360 and arguably PS3) are played by hardcore gamers, while social, music, and puzzles are played by casuals. This is very ironic, since the most popular shooters, Halo and Call of Duty, are widely played because of how quick and easy their matchmaking systems are. Games with more detailed gameplay like Killzone or more complex interfaces (most PC games) are shunned every week in mainstream podcasts like Invisible Walls or Epic Battle Axe by self-proclaimed "hardcore gamers."

Before this hideous, horrible generation of video games started, and the terms hardcore and casual along with it, a hardcore gamer to me was someone heavily involved with the modding community on counter-strike, or playing Japanese imports on a modded PlayStation. A casual gamer, to me, is someone who plays popular games every now and then, a couple games online here and there, and maybe sometimes dabbles in deeper games like Bioshock or Fallout 3, but then again, they probably wouldn't touch either of those or Mass Effect if those games weren't so much like the shooters they venerate.

People who play iOS games or Facebook-type browser games aren't "hardcore" or "casual." They're simply not gamers.

So saying the DS or PSP is more hardcore than the other isn't entirely fair. Both games have plenty of awesome experiences to immerse yourself in, a lot of traditional games that explore the boundaries of their respective genres. Summoner of Leviathan made an awesome point about Pokemon - it clearly has the casual appeal, but I'm playing Heart Gold right now and I'm stunned at how many options and concepts the game throws at you to lose yourself in. To me, that's just the hallmark of a great game designer.

Well, this is definitely a matter of opinion and if I had to weigh in on either side I would go with the PSP. Out of the RPG's I've played, even Pokemon with all of its options doesn't come close to how deep PSP titles are, which is why I feel like I'm playing "Big Boy RPG's" when I go back to my PSP. Tactics Ogre: Let Us Cling Together just came out last night, and it can be added to the growing list including Metal Gear Solid: Peace Walker and Valkyria Chronicles II, single games that blow every DS game out of the water. THe DS has more "pick up and play" allure, games that are specifically made for handhelds, and certainly a lot of PSP games fail because they try to be like console titles. But for games like Gran Turismo and Motorstorm, the console experience actually fits extremely well on a handheld, and if you can make games like Metal Gear fit that mold, and still have the same quality as the console experience, why would you ever go back to anything else? Ok, obviously that's a dumb statement cause I've gone back to Pokemon, but I was very dismissive of the PSP in the past and getting one in the last year totally changed my opinion on handhelds.

But like I said above, you can't totally dismiss the DS, hardcore gaming is a mindset and not tied to any platform. I know friends with 360's who only use it for downloadable games and mostly puzzles at that, I'd say they're far more casual than my friend who just got into video games and is playing Pokemon on her DS. Nirojan's ultimate question, which console would hardcore gamers lean towards, is a clear cut case for me, but both machines have withstood an usually long span of time, and still have awesome games coming out every year. You couldn't do wrong with either.