During the BSD lawsuit, free software was not widely understood, the company doing the suing (AT&T) was one of the biggest in the world, and the one being sued (BSDI) was a nobody by comparison. It was clear that AT&T had grounds for a real case. Everyone I know that was there says that there was real fear of the outcome. And I've known a lot who were there.
By contrast when the SCO lawsuit happened, open source was far better understood, it was a small company (SCO) doing the suing, and the companies being sued were the biggest in the world (starting with IBM). This threat was far less credible, and if it failed, everyone assumed that they would get lost in the shuffle.
It didn't hurt for the latter case that groklaw stepped up and there were endless well-informed people who said that the case was groundless. And no, I don't just mean nerds who read slashdot. But also most of the tech media, various interested lawyers, and so on.
Remember when SCO was trying to sue everybody over Linux? Why didn't the *BSDs become more popular then?
Linux being more popular then the BSDs had nothing to do with anything Legal outside of Linux being GPL.