BSD was in decent enough shape at the time to run on PCs. Though it fragmented early through no fault of Linux. And the AT&T lawsuit created a lot of FUD in the area without actually protecting System V. It's unclear if another thing would have popped up to fill the void... Linux flourished in the confusion, but without it, it's hard to know if something else would have been developed before the AT&T lawsuit settled.
But what really allowed Linux to take off the AT&T vs. UCB/BSDi lawsuit. At the time Linux, didn't have networking much less a window manager etc... so lot of people, mysef included (incorrectly thinking is was a copyright case) thought we were going to lose a UNIX for our inexpensice (i.e. 'cheap' 386 based systems) so we all started started to hack on Linux 0.99xxx [my first real serious taste was an early Slackware version on a billion floppies fairly soon after Linus made it available and Patrick pulled together his first distribution].
But ... (and as I have point out elsewhere - see
.... if AT&T had won the case, all the other UNIX flavors (Linux included would have had to have been pulled from the market).
So in many ways, this question is not really a fair one.
AT&T lost the case, and Linux got the ball and ran for it.
That said, I'll drop into the hypotheical, if AT&T had lost and Linux had not been there ..... then... I do think some flavor of BSD would have been the winner. The two wild cards are from Sun and OSF/CMU. As Larry says is what about SunOS and Solaris, although the legals of Sun doing that I wonder. The other question is Mach/OSF (I know Larry does not like the codebase).
But one of the *BSD, Mach or an FOSS Sun code base would have had the most legs.
Clem