Usenet: You are connected to a server and downloading, not uploading. Therefore, even if caught you could never get blamed for distributing data (and that hurts the most if you are taken to court). However, if you want to really take advantage of Usenet, you need to pay a monthly fee, and obviously, your personal info is in a database somewhere, basically proving that you are using the service. A raid of Usenet account servers by law enforcement would not be a good thing if you are a subscriber.
BitTorrent: Free, but you are completely naked. You can see everyone and everyone can see you. Apps like PeerGuardian can decrease the chances of you getting busted, but nothing is 100% assured since companies who monitor this stuff generate new IP's constantly. Everyone who downloads is uploading. Even if you set your upload speed to no more than 2kbps, you are still technically uploading, and therefore could be sued for contributing to the distribution of pirated stuff.
BitTorrent: Free, but you are completely naked. You can see everyone and everyone can see you. Apps like PeerGuardian can decrease the chances of you getting busted, but nothing is 100% assured since companies who monitor this stuff generate new IP's constantly. Everyone who downloads is uploading. Even if you set your upload speed to no more than 2kbps, you are still technically uploading, and therefore could be sued for contributing to the distribution of pirated stuff.