I think part of it stems from the fact that Media sources know that the Republicans are vindictive and will extract a price if they report on stories that embarrass or humiliate them - while Democrats generally will stop and try and figure out whether its a valid story at the point (see for example the range of opinions on Al Franken). The Both sides do it argument sort of gives them cover?

...in the last two hours I've heard three different calls on NPR to reassess the presidency of a man who has been out of office for 17 years...surprisingly, not one mention of the serial predator who is currently holding that once august position.