This inquiry is from a financial standpoint regarding Microsoft, Nintendo and Sony and seeing as the casual market is larger overall, I'd have to say it's more important; however the core market as a whole usually remains loyal to each respective console manufacturer and can make a difference overtime. So seeing as they both have their own set of advantages what's your take?   

A healthy combination of both is the obvious answer for me.

Edit; Rol: would the core gamer enjoy and spend a lot of time with Wii Fit (on average) and would the casual gamer enjoy and spend a lot of time with RPG's and FPS games (on average)? Likely not. People who only play Angry Birds on iPhone or Nintendogs will probably not be in the demographic of Portal 2 and someone who spends his entire life immersed in a MMO will probably care little for feebleminded mingames with no apparent objective and substance.

Gamers are very different (which you also state yourself) and I can easily see "core" and "casual" as two separate markets. Your grandparents' generation are unlikely to buy Gran Turismo 5 for instance, or do people still claim that casual games draw people into and drive them towards "heavier" stuff? Someone who is not quite taken with gaming as a hobby and time consumer will never ever sit down and start playing Neverwinter Nights 2 all of the sudden.

There should be a separation there.  Core is more important to the development of the industry as a whole, really to any industry.  This is the same reason that automobile companies build race cars and compete in Le Mans and the like.  It makes for better progress and pushing new boundries, which eventually trickle down to all gamers, core and casual.  Just like hardly anyone gets behind the wheel of a race fit Ferrari or Audi, but other Ferrari's and Audi's benefit from the engineering.  Casual is important to keep the money flowing which will allow more core to be created.  There are crossovers obviously, but in general, this is how I see it.

The casual market obviously makes alot more money, the games look like the were piss easy to develop with hardly any cost but sell like mad, but BOOOOOOOOY is it BORING. keep it away from me.

i prefer the core market but both are as important as each other. 

for a company, ever since facebook and the likes got the internet a popular place to spend your day, casual gaming (especially the short app type) got way more desirable than regular gaming. This is where the real growth will continue to be in recent years.

This is also why devs that touch the PC should be more prolific in bridge games with low spec requierments, because that crowd already has a PC and could graduate there. Heck, do a facebook app tied in with an easy to get (DD) and easy to play game, it'll sure help jump the gap. I played an indie game recently that let you posts your scores on twiter and facebook... that's an other way to do it and i'm sure it'll work, bring full casuals using not so casual players to bait them.

for consoles... well yes it is as rol says, they need a broad appeal.

Imo casual market brings in more money, but the casuals can be easily swayed to a better looking product that offers more functionality, ie no brand loyalty, whereas the "Core" players have some kind of brand loyalty and will likely purchase the next generation console and not just go with whatevers the hype at the present. Core look at specs and the games that the system has to offer whereas casuals just go with whatevers the trend and whatever is family friendly, I don't think prior to Kinect launch many would look at 360 as a family friendly system, yes let's sit down and enjoy some Gears of War as a family.

Casual, undoubtedly. Why? Having an attach rate of 20 doesn't mean much when your console only has a userbase of 50k.

EDIT: Obviously, though, if you get both of them, like Nintendo, MS and Sony are trying to, then nothing like it.

I would definitly say the core is the key to being a success. and having a smaller casual fanbase is also good but not as important. why?? because the casuals buy a few games and then play those games throughout the year. you hear about a lot of people who played the Wii and now have it on a shelf at home.

the core is more important because they keep buying games all year round. someone like me will continue to buy like 7 or 8 (probabily a lot more this year) new games this year, which supports the developers and keeps the industry going. the other problem with the casuals is  what someone here else said - will they abandon the product if something better comes along?

possibly, i dont think anyone can tell at this point tbh, because the Wii and Kinect are doing well at the moment.

I suppose you mean important to console makers (SONY, Nintendo, Microsoft) specifically in which case I would say a good balance is needed, but casual is more important especially today. Like it or not Casual games sell well and cost a lot less to develop on average and no game or console can be a success without a large number of "casual" gamers the PS2, PSOne, Wii, DS, SNES were all market leaders because they managed to capture the casual audience. And with the success of the iPhone and face book games I could see a greater shift to attract ever more casual consumers to gaming as that is where the money is. 

Casual has always been important. There hasn't been a generation winner that hasn't relied on the casual gamer to some extent.

We're yet to see a hardcore only console win though...