The Seven Liberal Arts (the original ones) were generalizable intellectual skills; the new Liberal Arts, with a couple of exceptions (language and mathematics, which, in modified form are part of the old Seven arts), are simply subject areas or "disciplines." The old Liberal Arts are intellectual skills that are applicable to every subject in the curriculum; the new Liberal Arts are each the study of the body of knowledge and methodologies applicable uniquely to that particular field.
The proviso here is that the first three of the old Seven Liberal Arts (the "trivium") are more universal than the last four (the "quadrivium") which are sometimes considered subject areas, although the better way to look at them is to consider the trivium generalizable linguistic or qualitative skills and the quadrivium generalizable mathematical or quantitative skills.
Although the Seven Liberal Arts are skills, they are skill ordered to knowing rather than skills ordered to some practical utility. The new arts are mostly intellectual as well, which is why some of them are anathema to the people who want to turn our academic institutions into vocational learning centers.
Both lists are useful, but they serve two different functions.