According to Giganews' own marketing data Usenet is definitely the clear leader. Listed below is the percentage of time Usenet was searched for compared to the overall search data for Usenet and newsgroups.
Searches for Usenet
2003 - 52.35%
2004 - 67.95%
2005 - 55.15%
2006 - 53.25%
So why would people use the word Usenet more often than the word newsgroups? I believe there are two primary reasons.
Wikipedia® defines Newsgroup(s) as "a repository usually within the Usenet system, for messages posted from many users at different locations. The term is somewhat confusing, because it is usually a discussion group. Newsgroups are technically distinct from, but functionally similar to, discussion forums on the World Wide Web."
In this definition we see the fundamental problem with the word newsgroups. In many people's eyes the word newsgroups can be confused with web based applications like forums and discussion boards. Services like Google Groups and Yahoo! Groups which provide a blended mix of text newsgroups and their own "create your own" groups which are not NNTP based further confuse the issue.
Since full access Usenet services like Giganews are far more popular than text only newsgroup services the word Usenet seems to be a more natural choice when referencing the technology.
Another reason for Usenet's dominance may be a communication issue. I’ve been to many conferences representing Giganews and from time to time you run across someone who says “What does Giganews do?”. When I respond with “Newsgroup services for individuals and ISPs” they quickly respond with “I know what newsgroups are. I read CNN® all the time!”
Obviously some people are trying to infer meaning from the word “newsgroups” that isn’t there, so perhaps a communication problem has created a shift to the more specific reference “Usenet”.
In any case, it seems like Usenet is clearly more popular and may be a more descriptive term when referencing the NNTP network. This is especially true as web based text newsgroup applications further dilute the definition of what exactly a newsgroup is.
Which term do you reference when you talk about Usenet?