I used the Swiss for outlining and the lines turned out thinner with the same needle grouping... Had the same results with the Bishop. Slicksteel explained why in another thread:

As you are useing a clip linear machine you are actually get a true needle stroke. On coils,direct drive rotarys,swash drives you will get a bigger line as there is more wobble.
look at the needle grouping and then the line, standard groupings needle tips are actully very thin if you loop it, we are just used to a coil machine making a bigger line as the needle tends to jig about in the skin causing a fatter line.