BitTorrent is the best because it's not a service that rests and depends on the servers of a single private company. It's all about sipping small downloads from ad-hoc servers. Dropbox is a commercial venture from a single company, and while they're handy, that makes them a single point of failure if and when they go under. BitTorrent wins.
I have used both a lot, but I would have to say that I like Bit
torrent much more than Drop box. Drop
box has way too many limitations. You
can only upload a certain amount of content and you have to pay when the
content rises past a certain amount. Bit
torrent is just easier to use.
Bittorent is by far the better option. It is a matter of the material available and the access granted from other users that makes Bittorent so great. Over time Bittorent may not last due to copyright laws but while it is around it is by far the best file sharing option there is.
BitTorent is better. However, I think that they are both good products to have on the Internet. BitTorent is used for file sharing and Dropbox is used for off line file storage. They both do a great job in what they were designed to do. I am fond of BitTorent because of the ability to share.
Dropbox is the best thing that has happened for my professional life. I can instantly save and pull up items from my house laptop, my phone, my ipad, my work ipad, and my work computer. Dropbox has changed how people really are able to share their files and keep things organized.