I find the term "core gamer" unappealing, for a specific reason: it seems to have no clear meaning, and people define the term as they see fit to bolster their arguments.
If the term IS to have any specific meaning, it would need to adhere to specific, well defined principles. I think we can generally agree on those: a concern for the technical advancement of gaming -- whether that be through network connectivity, graphical advancements, improvements in physics, or otherwise -- as well as a concern for complex, precise, and challenging gameplay.
The argument for PS3/360 in this thread has been, by and large, an argument for comfort and accessibility. You can sit on your couch and play them. They work right out of the box, no questions asked. As nullpointer said, it's more "inviting," or as Asmodai said, it's more "comfortable." Now, I want to emphasize, first, that those concerns are fine. If that's what you care about, that's cool. There is no right and wrong here. However, if we specifically want to talk about core gaming, then these concerns go directly against "core gaming" values. You are sacrificing better network connectivity, better graphics, more precise aiming, and other concerns so that your gaming can be more accessible, inviting and comfortable. Since many people seem to be highly concerned with self-identifying as "core" gamers, you're going to have to reconcile this conflict.
Of course, the best solution would be to simply abandon the term "core gamer" entirely, but everyone is too invested in using the term as a wedge to belittle "casual" gamers, so I suppose that isn't possible.
