High quality streaming, like Netflix, uses a lot of bandwidth.
In fact, Netflix now consumes a very significant portion of all bandwidth in the U.S.
This is the main reason that companies like Comcast and other providers are trying to cap bandwidth usage. They didn't really care until Netflix came along, and of course they also don't like the fact that Netflix competes with them for selling content.
In comparison to Netflix usage, the people who download files with BitTorrent and other file sharing services don't use nearly as much bandwidth in total. This is not to say that they couldn't be using as much bandwidth (although peer-to-peer technology, which is commonly used for downloading, is limited by the fact that the uploaders don't have the resources to deliver as much bandwidth as Netflix).
Also, if the question you're asking is if you were to stream a movie or download one of similar quality, which would use more bandwidth...
Well, the streamed one would probably use more bandwidth, because it can't use the same kinds of compression that a movie you download can. A movie that you would download before watching can (at least in theory) use very high levels of compression and less error correction (which takes additional bandwidth) than a movie you'd stream.
Don't listen to the anonymous guy who said that streaming uses more bandwidth. He's comparing apples and oranges - infinite stream (e.g. watching a TV channel online) and finite file download (e.g. downoading a movie).
To really answer the question you have to compare the same thing. So let's say it's a movie, the same movie. In that case it depends on the speed that the website is willing to offer you, but most of the times download is faster, which means it uses more bandwidth for a shorter period of time. Whereas streaming uses less bandwidth for a longer period of time. In the end you will download the same amount of data, since we're talking about the same movie.
There are other things that can influence the answer. For example, if you're downloading a torrent the speed will depend on how many people are sharing it, their connection speed etc.