Well the truth of the matter is that like everything else in Photography there isn't a correct answer. It's really a preference and although this preference does make the subject look and feel different, you can't really say which is the right way or which method is the correct use of equipment. It's like lighting, could you say Loop lighting is correct and Rembrandt is wrong? You can't... it's a style and a method which can be applied in any circumstance.
Even with that said though you could say that there are times when certain equipment is more often used then others (maybe you can consider that to be the reason to consider it to be the correct answer but I wouldn't).
Generally speaking an umbrella has a wider light spread than a softbox, and this is true whether you are choosing to use a shoot through umbrella or a reflective umbrella. With softboxes, the distance of the light falloff is much shorter. Umbrellas generally give a greater contrast while softboxes like its name, gives you a softer effect that softens even the shadows.
One general characteristic you will find in umbrellas that is not as problematic compared with softboxes is to do with "hotspots". With umbrellas you tend to get "hotspots" (where lights concentrate in the middle of the area lit), and with softboxes because the light is more contained by the way it spreads (due to the construction of a softbox and the diffusor), you tend to get a more even light on the lit area (the downside is greater light falloff (meaning greater distances between the light and subject will have significant drop in light).
I have seen people use softboxes to light up a close up portrait and then again I have seen people use an umbrella to do the same with the similar amazing results. Once you have experience with softboxes and umbrellas you will understand that you can't really categorize one for certain specific scenario because it depends on many variables you are shooting for.
Ex. I would never use umbrellas to shoot products, but I have seen people use umbrellas to shoot products. I never use a softbox to light a face (mainly because I believe the contrast which an umbrella gives to shadows sculpts a subjects face giving it much more definition than a softbox), but I have seen many great photographers light up a face with a softbox. The only time I may use a softbox to light up a subject's face is probably during a glamour shot for a cosmetics ad. In this case I want the skin to be smooth and shadows and dark contrast may not be something the client wants.
In this photograph of Bloomberg Anchor Susan Li, the photo was shot with a Photek Softlighter II. This umbrella is often used by celebrity photographer Annie Leibovitz and that especially during the Louis Vuitton Campaign shot by Leibovitz. The Softlighter II is a bounce shoot through umbrella. The main reason for it's popularity is due to its short light falloff distance, and the softness it produces while retaining a strong contrast between shadows and highlights.