NEW YORK — Fox News Channel for the first time defeated archival MSNBC in average primetime households for the week of Jan. 4-10.FNC averaged 215,000 households for the week in primetime, according to Nielsen Media Research, while MSNBC averaged 199,000 households. While FNC does occasionally beat MSNBC in ratings, it has had a tough time earning more households than MSNBC because FNC is carried in almost 10 million fewer homes than MSNBC. For the week, FNC averaged a 0.6 rating in primetime, topping MSNBC’ s 0.4 rating. CNN won the battle of the 24-hour news channels for the week. The granddaddy of news channels snared a 1.0 rating and 786,000 households. CNBC followed with a 0.7 and 468,000, and Headline News got a 0.2 and 165,000 homes.