Ned Block (or is it Bill Maher?) gives us a good statement of the fundamental problems of consciousness and talks about some of the most commonly cited neuroscientific findings and what they mean about consciousness, and specifically what he takes to be Dennett's position that consciousness is an illusion:
"The hard problem:" how is it that the neural basis of an experience is the neural basis of that experience and not of another experience? Patricia Churchland, in the article I linked to, responds to this:
What is an example where a science — any subfield of science — explains why X = Y? Not how we know or why we believe that X = Y, but why X is identical to Y, rather than to Z. Using the examples already at hand, the corresponding questions would be these: why is temperature mean molecular kinetic energy, rather than, say, caloric fluid or something else entirely? Why is visible light actually electromagnetic radiation rather than, say, something else entirely, say, ‘‘intrinsic photonicness’’? By and large science does not offer explanations for fundamental identities. Rather, the discovery is that two descriptions refer to one and the same thing — or that two different measuring instruments are in fact measuring one and the same thing. Why is that thing, the thing it is? It just is.
Block's substantial point here is distinguishing between access consciousness, defined as "information globally available in the cognitive system for the purposes of reasoning, speech and high-level action control," and phenomenal consciousness, which is consciousness as we experience it.
Interestingly, Block uses many of the same neuropsychological cases cited by Dennett (like blind sight, where someone claims not to be able to see something but yet can identify it if forced to guess), but whereas Dennett uses these cases to say "look, you think you know what you're conscious of, but you're really not," Block says this shows that what Dennett (or any functionalist) calls consciousness doesn't correspond to what we experience, and it is still a legitimate challenge to the theorist to explain this experienced world that the functionalist in effect ignores.
It is confusing, however, when Block sums up his point by saying (at 3:38): "what we need to do is distinguish the cognitive aspects of consciousness from the basic biological phenomenal aspects." This sums up a methodological difference: Presumably Block wants to find the biological underpinnings of phenomenal consciousness. Dennett and Churchland both argue that because our self-reports are unreliable, we need to somehow pin them down in third-person verifiable (i.e. scientific) language before we can then look for the neural correlate. For instance, in the "inverted spectrum" case, Block claims that its conceivable that you and I could have switched colors: my experience of yellow is your experience of green, but yet we use our words the same, so this difference is undetectable (we both point at grass and say "green"). The response is complicated, but amounts to a claim that any such switch in perception can be detected with enough testing due to the nature of color as a network of infinite interrelated shades; you can't just shift the whole spectrum towards one end without this showing itself up in effects in the person's ability to discriminate certain shades or make claims like "lighter" or "darker" accurately or whatever. So the full explanation of what's going on, for Dennett, has to involve getting behind the phenomenology to "what's really being seen" despite the person's self reports, and from there you can figure out the neural correlate.
Since both Block and Dennett in effect acknowledge both kinds of consciousness, and are certainly not going to shut down some line of research if it's actually achieving results, the dispute to me seems more a matter of emphasis and the use of language than anything else. This is a conflict among people trying essentially to do the same thing rather than some showdown over fundamental ontology.