"It varies from the big 3" for me.
To understand this, I have to define what is "core" and "casual." The "core" are what we stereotypically think of as gamers. Males aged 5 to 40 who play games as their hobby. If they aren't working, socializing, or attending to family needs, you will find them in front of a television or computer screen.
Your "casual" gamer is who none of us would consider a gamer. The games they choose to purchase are purchased on whim or due to fad and advertising. They play sparingly less than 2 hours per session. The games they play are not overly deep, instead they are more like NES and SNES games where you can pick up and play at any time without worrying or spending anytime getting reacquainted with the story, progress in the game, or the mechanics of the game.
The "core" is important to all three in different ways. Nintendo's "core" games (Mario, Zelda, Metroid, Donkey Kong, and on) are not overly complicated games. They are platformers or action-adventure games where one can pick up and play them at any time. Too often, Nintendo's "core" games are viewed and ridiculed as "casual" by "core" gamers. However, I am sure Nintendo could care less what Sony or Microsoft's "core" thinks when their "core" games are outselling Microsoft's and Sony's by a margin of 3:1 or more.
In contrast, the "core" games for both Sony and Microsoft are very complicated games. Gears of War, Killzone, Gran Turismo, Halo, Mass Effect, Call of Duty, Fable, God of War, Uncharted and on. All are complicated because they require at minimum, a level of expertise in controls. Digging deeper, to fully enjoy them one needs to immerse themself in the background story and have a comfortable level of familiarity with the mechanics of the game such as "jump height, XP, RPG stats, aim down sight speed, reload speed, and on." One cannot pick up and play these games, one needs to practice them to be good at them.
The "casual" market is preeminent undisputably because it is a market without limits. Nintendo has shown this and Microsoft is showing this with the Kinect. Tapping into the "casual" market requires a back to basics focus on instinctual, easy to learn, hard to master gameplay and multi-million dollar advertising campaigns to reach everyone on up to grandmothers and grandfathers.
In contrast, the "core" market has very firm limits as Sega and Atari have shown. To use an analogy, catering to the "core" is equivalent to catering only to the drama club and music club in high school, while catering to the "casual" is catering to the entire high school. Yes, catering to the "core" will get you a guaranteed amount of the pie, but you are only getting a few pieces of the pie, while catering to the "casuals" gives you a greater chance to not only get the "core's" piece of the pie, but even more on up to the entire pie.
Without a doubt, both markets are important. The "core," if you please them will remain loyal to the extent of rabidly defending you on the Internet. The "casual" market is the future, it is marketing to entire populations in nations. However, the "casual" market is not to be relied upon. Like fashion trends, what was trendy yesterday will be remembered with chuckles and "Oh I didn't buy that" type banter today. The "casual" market may get you bigger profits, but future profits with similar marketing techniques will not be guaranteed tomorrow.
Or to use gamers language, you can bet with near 100% certainty the "core" will buy more than 2 new games each year. Chances a "casual" gamer will do that is 50% or less. However, there are and will always be more "casual" than "core" gamers.