The lumiquest is a softbox that mount directly to your flash. It might be able to be used with the flash on the camera, but maybe not. It could certainly be used with the flash on a stand. You would need an adapter to mount the flash on a stand.
An umbrella has to be used with the flash on a stand or something and does need an adapter.
The Lumiquest softbox is rather small, which is good when you want something that is handy and can be packed with you. However, the softness of light is determined by the size of the light source...bigger is softer. So when comparing this to an umbrella, the umbrella will give you light that is quite a bit softer.
Comparing an umbrella to softboxes in general (usually for studio lights)...I like softboxes because they constrain the light to one direction and a certain degree of spread. An umbrella tends to spill light all over the place, which can be a pain in some situations...but their wide spread can be great for large group shots.