I've found that, in general, Australians pay a lot more attention to all cricket whereas England tends to focus in very much on the Ashes.
Obviously, thats the series that is the most important to both countries and when it's exciting, there is very little that can match it. But Australia seems to care, and focus, on each series and winning that series. England's focus seems to be 'well, we'll treat all these tours as tryouts for the Ashes.' It's up to them in terms of what they see as most important, but I don't think it benefits them to be so singlularly attached to one series.
Australia always pays a lot of attention to the tours to subcontinent, which a lot of players don't personally like visiting (no night life, different culture, etc). But Aussies tend to try to make the best of it, whereas English players just want to find an excuse to pull out.
Anyway, I agree that Ashes are the most important to both countries and its OK to have favorites, but I don't know if such singular focus is a good thing.
I'm not singling out any English fan on this board, since a lot of them here are some of the most knowledgable about the game - but thats just the feeling I get when listening to most english fans or their media. Maybe an Englishman would like to give their opinion on this? I know about four or five English cricket fans personally, and they all pretty much only care about the Ashes. When pakistan visited, it was all about 'well yea, he is doing well but how's he going to do in the Ashes?'. Even in SL or India, "Yea, well Flintoff is doing well in India, but maybe they should let him rest in all Tests until the next Ashes." That type of thing. Of course, thats just anecdotal evidence - but it seems to be corroborated when I hear a lot of the commentary by English media (on air and paper commentary). Nothing overt, but just a general feeling of 'Yea, but what about the Ashes?'