How much more does the Dokdo (독도) / Takeshima (竹島) / Liancourt Rocks issue matter to Koreans vs. Japanese?

It's actually quantifiable to a certain extent. First take a look at this page:

It gives 94 million Japanese internet users to 35 million for Korean, almost 2.7 Japanese for every Korean on the internet. Now do a search on Google for 독도:

8.16 million hits. Now a search for 竹島:

2.9 million hits.

That works out to about 7.5 times more content in Korean per person on the islands than in Japanese.

And on Google News you also get the following:

1,021 news articles in Korean in a search today, and:

145 news articles in Japanese (7 times). Factor in population and that gives 19 times more content in Korean per capita than Japanese.

The rough conclusion you could make from this is that: Koreans care way more per person about the issue than those in Japan, and the media even more so.

See the Wikipedia page on the islands here.