the bigger the root the better the plant establishes. so if given a choice I'd go for the root every time. but to increase my stock I would divide the root stock.

As Seaburngirl says, you would normally divide ferns at the rhizome (root) or grow then from spores (the fern equivalent of seeds) if you want to reproduce them.

No fern is able to grow from a cutting, in the way that woody plants can, although some can produce fern-lets (baby ferns) if you take a frond (the full stem + leaf of a fern) and weigh it down into the surface of very moist seed compost. The whole thing must be completely sealed in an airtight polythene bag to keep the humidity as high as possible, and away from direct sunlight. If you're lucky the fern-lets will grow out of the frond after a few months and can be separated and potted up after about a year.