I never thought I'd say this, because I've always disliked elements of Quark (such as, my pet hate, command-k to delete... rather than the delete key), but now I think it comes down to the type of designer you are. Different tools suit different people.
I've been using both for more time than I care to think about, and have favoured ID ever since I started using it with v1.5. For me there is no competition, but I'm very used to Photoshop and Illustrator, and design with layers, etc. The thing I love about ID is the fluidity of the design process.
Apart from the obvious (already knowing Quark inside out), other people that I have worked with are much more traditional in their approach, and simply aren't interested in what they see as ID's unneccessary "bells & whistles". I have worked with very good designers who ONLY use Quark (as in no other applications at all!).
I do quite a lot of freelance in and around London in very well established agencies, and have found that Quark is seen as a trusted work horse, whereas ID is still to earn its stripes. Many designers (and more importantly, art directors) appear to have tried ID in its early days, but were put off because it was too feature packed (slow) for the hardware it was being run on.
Ironically, the only strength that Quark has over ID, a strength that ID will never be able to compete with, is that Quark is less sophisticated. It's a difficult fight for Quark to win; stop developing the product in the hope of retaining a percentage of designers, or try to take on the might of the Adobe integrated toolset.
I know who my money's on... I don't think either program is perfect, but I think ID's imperfections will be addressed much more quickly.