Is it OK to change my answer? I thought about this a little more and examined my portfolio and saw that I actually have more "net" names than I do "online", so there has to be a reason. Some of my favorite "net" names are not .coms, but rather, .info's, which I think go well w/ "net",(ie netdr.info, netmd.info). Additionally, other than single keyword names, the quality of the name, relative to traffic, depends upon the number of searches for particular word combinations, (as in 2 and 3 word names combined w/ "net" or w/ "online"), and not based upon the single keyword value alone, although OV results and Google links can help in measuring a word's general popularity and how familiar of a word it might be to the internet public.
That being said, on the net vs online question it would all depend upon how the words fit into the context of what the site was doing, the ext, and how the "net" or "online" looked w/ whatever it was combined w/. Just too many names and variables involved and too broad and sweeping a question to give a specific, definitive, "this one or that one", answer to, IMHO. The possible variables involved, are worth discussing, however.