You have more control of the light as its more contained. I use shoot thru umbrellas and softboxes and brollies work fine a lot of the time for me but sometimes the light that gets bounced around when indoors can be an issue. If I want the light to fall off quicker and focus more on my subjects without lighting up the environment so much, the smallish softboxes do the trick nicely.
You also avoid lens flare from the light out the back of the brolly too. Outdoors if in the open its not so much of an issue for me, and I can just feather the light a bit by pointing the brolly over their head a bit. But I still don't get the same look as a softbox exactly.