I try to target both. If your website can rank for short-tail, generic keywords then target them. If it cannot then you have no choice but to target the long-tail, specific keywords. One way I determine if I can rank or not is to head over to SEOMoz and pull a keyword difficulty report for the keyword I am considering. Then I look at the top 10 websites and compare their domain and page authority to mine. If I am competitive with their scores I'll go after the keyword. If not then I keep looking. Hope this helps.