By "linking" do you mean having separate objects moving attached to a frame of some sort?
If so, this is what I've heard called "segmented mesh," and I first remember noticing it in Tomb Raider. Indeed- this is what first prompted me to start researching skinning because I realized that if you just had polygons between the segments it would (ok might) look a lot better. It would certainly look fancier.
Modern skinning though uses some number of weights on each vertex. Therefore it is much more expensive to render the objects, since you're transforming each vertex by a number of matrices and then doing a weighted sum, as opposed to just transforming the vertex by one matrix. (Which as it turns out is how our first-gen skinner worked, all verts had one weight, so the "joint faces" were the only ones that would deform.)
Capabilities gained or lost? The only difference in the end result is how they look.
Specific situations where I'd use one or the other? I'd use skinning if the jointed look didn't work or was otherwise noticeable and undesirable.