TCR is a parody of conservative news shows (e.g. The O'Reilly Factor). TDS is more of a parody of news in general.
Colbert pretends to be highly conservative, as tends to be the case in the modern Republican party, while Stewart makes no attempt to appear anything other than liberal.
Because he is rude, condescending, ignorant - just like members of the Republican Party.
HORSE BONER
Stephen Colbert acts like a republican while Stewart doesn't even try.
Colbert has a gun; he makes conservative comments and criticisms of the "liberal" side of politics; he deosn't like to share what he has and believes he deserves more than others because he's superior.