Neither BSD or Linux are "Unix" but they are both reasonable replacements for it
None of the various incarnations of BSD or Linux have recently passed the certification required to be UNIX(TM). Nor do they have any source code which came from any AT&T Unix release which wasn't made freely available at some point. As I remember it, the only reason that the *BSDs are even around is because AT&T lost in their legal efforts to claim there was any protectable Unix source code in 386BSD which would have allowed them to stop the initial release. Prior to 386BSD, to make a functional BSD system; you had to include some AT&T owned Unix source code and have a bonafide Unix license. Any modern BSDish system which anybody uses was derived from the original non-infringing 386BSD. Amusingly, BSD no longer being Unix-based happened at the same time as Linux appeared (1991-1993 time frame). I was at a Usenix conference around that time when BSD/386 (a proprietary fork of 386BSD) was announced and saw the BSD/386 guys blasted by Bill Jolitz for taking his efforts to make a freely distributable BSD and immediately make a proprietary system out of it. That pretty much cemented my switch to Linux from BSD-based systems.
AT&T vs UCB lawsuit: I seem to recall that there were some very minimal amounts of AT&T derived code in 386BSD; but at the same time AT&T had grabbed a lot of BSD's code for networking utilities, etc. without following the required copyright license. UCB, as a result, countersued for copyright infringement against AT&T. When the dust settled, BSD remained freely distributable. So BSD was once Unix, but I think you would have decide the "Ship of Theseus" question in the positive; to say modern releases are. While the Linux kernel to the best of my knowledge never had any Unix code it, many early network programs in Linux distributions were ports of the BSD code. So at that time, you could say that Linux distributions were derived from BSD which was derived from Unix, so Linux distributions were Unix as well. :-) Unless, you decide the "Ship of Theseus" question so that modern BSDs are no longer Unix. How about we just agree that they all do a good job of filling the same niches that "real" Unices did and more.