For the adjective meaning with skill or having skill, skillful is the preferred spelling in American English, and skilful is preferred in all other main varieties of English. Skillful appears with relatively high frequency in Canadian publications, but the ratio is still 4:1 in favor of skilful. Aside from spelling, there is no difference between the two words.
Many of his essays and stories would benefit from skillful paring. [Wall Street Journal]
Two of the most skillful here, Akira Yamaguchi and Manabu Ikeda, cover vast canvases with a miniaturist’s level of detail. [Washington Post]
The most impressive elements of Shogun 2 aren’t its fantastic graphics or its skillful evocation of Japanese history. [AV Club]
Outside the U.S.
He is acknowledged to be one of the most skilful procedural experts to hold that office. [Vancouver Sun]
The writing is skilful if you are into Satan fantasies and blood-flecked sex. [Daily Mail]
It was rugby at its best; fast, combative, skilful and with great tension. [The Daily Herald]