I would vote for the softbox in that instance.
The softbox is an enclosed reflector, so there is very little stray light spill, and we assume all of the light goes forward to the aim point (it can't go anywhere else).
But stop and just look at a CFL lamp in an umbrella first. Of course most of the CFL light will go out sideways from the bulb, totally missing the umbrella altogether, which is very extreme room stray light. Not a good thing, and the light loss is not a good thing either. Not so much of it actually goes into the umbrella, so much less of it is reflected back.
I am not knocking umbrellas at all, they're great, and I am a fan of reflected umbrellas. Shoot-though umbrellas do have great amounts of stray light spilled into the room (maybe 1/3 goes through, and 2/3 is reflected back). But shoot though is used very close to subject, so the subject path is maybe one foot, and any spill reflections from room walls are several or many feet, which is an extreme difference, so the spill, while present in large amount, is minimized.
Generally a reflected umbrella is used with some type of reflector on the light to contain the light to actually hit the umbrella (for example, a speedlight with its fresnel lens at 24 mm), greatly reducing the stray spill.