Google Trends says the Heritage Foundation is winning the battle for traffic among prominent Think Tank websites, followed by the Cato Institute, Brookings and then the Center for American Progress.
Note: Heritage.org traffic rose sharply immediately after the launch of the Heritage Foundry blog in early 2008. I'm not sure how much of a causal connection there is, but it's very likely that the blog (a) improved their daily visitor traffic, (b) improved their Google visibility, and (c) led new blog readers to explore more of the Heritage site.
However, there is an interesting complexity. The Heritage Foundation and the Center for American Progress are both 501(c)3 organizations, focusing only on policy analysis and education. They "may not attempt to influence legislation as a substantial part of ... activities [and] may not participate in any campaign activity for or against political candidates." That sharply limits their ability to use the information they collect effectively in the blogosphere or in audiences outside of policy, academic and some narrow media communities.
However, political advocacy and campaign activity are fuel to bloggers and internet activists. So, the Center for American Progress set up a separate 501(c)4 organization: the American Progress Action Fund. 501(c)4 organizations can engage in political advocacy and "some political activities". The Action Fund produces the research distribution outlet, ThinkProgress.org, and the daily talking points newsletter, The Progress Report.
Look at how Think Progress compares to the Heritage Foundation.

These, not its own legally limited website, are the communications weapons of the Center for American Progress.
Rather than trying to consolidate power within a single bureacracy, they realized their goals required separate organizations, each specializing in one aspect of the larger goal. They have created one organization to play in the academic and policy world and a second organization to play in the media and activist world.
Differentiation allows specialization, and specialization allows...well, the kind of success you see above. This allows them to pursue multiple, coordinated paths to achieve their goals. As a result, the Center for American Progress is not so much a Think Tank as it is a Marketing Tank.
The lesson here is that, while organizations should think of information as an asset, but they should not necessarily assume they are also the best distributors of that information. The collection and analysis of information is a task distinct from framing, synthesis and distribution of information.
Note: the measurement tools are, of course, imperfect; consider this a best-available approximation.