A shoot through type umbrella is a pretty good poor-man's softbox, but of course it's not as good. It's much less light-efficient, you get far more spill, it works best when flagged, it will illuminate the back wall of the studio (assuming you're in a studio) almost as much as your subject which might add unwanted fill, and so forth. On location, they're so much quicker and easier to set-up and work with if you have no assistants, however. I do make use of them for exactly that reason. If you're going to use them thus, buy several different sizes and use bigger ones for placing farther away, fuller-length subjects, and/or softer light quality, smaller for the opposite.
Comparing traditional umbrella use to softbox use, the quality of light is different. A softbox generates light that is very soft but directional, with all the light coming straight to the subject from the front of the box. An umbrella is less soft (it doesn't get bounced around and diffused as much as light does within a softbox) but less directional, it wraps around the subject a little bit, more so the closer it is to the subject. So, speaking of a traditional bounce umbrella, the comparison goes like this: Softbox = softer, more directional light. Umbrella = harder, less directional light. This assuming that all other factors (such as head reflectors, etc) are equal.