First off, if Linux had a per-unit or similar usage charge, its adoption rate would all but certainly have been vastly lower. Factual basis: the many extant proprietary x86 Unix clones at the time Linux emerged.
There's the question of how to value "use value", and what the value of an OS actually is. Impressions are (IMO deceptively) skewed upward by the example of Microsoft, but it's the rare instance of a software-only mass-market OS platform -- actually, rare to the point of single-instance.
There's the question of what an ordinary or acceptable rate of return ought be.
And there's the question of how much of the returns should be shared with others.
Still, Linux as an enterprise might be compared with, say, IBM or Sun at their peak, possibly HP's server operations. There's the present valuations of Red Hat, Google, and Facebook, among other Internet companies based largely on Linux's capabilities.
Certainly multiples of billions in a traditional sense -- I'd argue for $5 - $20b.
Of course this is kind of speculation on one hand, but there was the Hurd project which might have taken off, or someone else could really have created something similar a year later, if it did not exist.
BSD had it's licensing issues, which today seems more liberating - most programmers seem to embrace it - but in 1992 was seen a free ride license which is something most Linux developers did not like. That's why Linux grew so much,. Saying that FreeBSD would taken that niche seems a little bit off IMHO.
Almost certainly, and also almost certainly FreeBSD. The UNIX Wars did more than anything to ensure that this didn't happen, though.
There's still a bit of an open question. Linux benefited over FreeBSD not only in not having a lawsuit looming over it, but in that its development process was far more open. Though it's arguable that FreeBSD is more stable (and for much of the 1990s had a superior networking stack -- hence its adoption at such shops as Yahoo), ultimately it was the addition of features, and drivers, to Linux which very much ensured its take-off, as well as the numerous distros, each of which had a slightly different focus (and often significantly different package management systems), some of which proved more attractive than others.
I find it interesting that of the two primary x86 unices, the more open one (Linux) beat FreeBSD, and of the Linux distros, a noncommercial and generally open one (Debian and variants) seems to be slowly trouncing the more closed corporate variant (Red Hat).
Around the time Linux was starting to make inroads into businesses. Usually by the backdoor - internal services needed platforms they could install without going through the usual acquisition processes. If it cost money, some beancounter was going to object. (I witnessed a couple of cases first hand.)
So the techies installed some flavour of Linux on decommissioned boxes instead and ran their systems where they could. Individually the cost savings were negligible, but when you suddenly find out that 30 or even 50 internal services are running on top of OS stack that had cost nothing, the upper echelons finally take notice. The fact that the OS could be customised and repurposed for a particular need was an amplifier, and only later became the core "feature".
I recall (with horror) the days when "tweaking the OS" meant running regedit.exe and turning a number of undocumented knobs in directions you could only guess at. Not to mention pray that the system worked on the next boot.
So Linux use began as a way to cut costs (or skip the acquisition process altogether). It ballooned because it was possible to customise and extend the system on the OS level as needed.
• Linux worked. It was "good enough". Once you reached the point of running a shell, GNU userland, an editor, and a compiler, it was off to the races. Not sufficient, but necessary.
• No lawsuit. The UNIX Wars put a multi-year crimp on FreeBSD. The BSD splits didn't help much either (these included not just the userland as in Linux distros, but kernel development --which for Linux distros remains unified).
• Freely hackable, but published changes are licensed under GPL. I don't know how much thought went into Linus's choice of license, but it proved highly fortuitous.
• The time was absolutely ripe. Even within proprietary Unix companies, people were advocating heavily for a freely-available, open-source operating system. See Larry McVoy's "The Sourceware Operating System Proposal", from his days as a SunOS engineer prior to founding BitMover: http://www.landley.net/history/mirror/unix/srcos.html
• Key early adopters and developers. Alan Cox on development, and John "Maddog" Hall at DEC were key in both pushing kernel development, facilitating early ports (to Alpha), and in putting legitimacy behind the effort.
• Multiple distros. Almost immediately a side-light of bundling up the kernel and a set of utilities into a usable package emerged: Boot Root, MCC, TAMU, SLS, Yggdrasil. I remember SLS ("soft landing systems") being explained, somewhat fondly, as "because it was a pile of shit". Eventually over a few months in 1994 Slackware, Red Hat, Debian, SuSE, and Caldera emerged, which with very few notable exceptions continue to rule the distro landscape. I find interesting that "bootable distros" were present from very nearly the start (my own first exposure to these was Linux Root Boot, a/k/a Lnxrtbt, on a single floppy, also Trinux, booting from 2+ disks into a ramdisk). LWN has a good early history: https://lwn.net/Articles/91371/
• As others have noted, functionality, cost, features, and exigency all meant that technical needs felt at the coalface by front-line engineering staff at many firms were being met with decommissioned server, or, very often, desktop systems. While Microsoft-bound CIOs were proclaiming "we run no Linux and never will" their organizations were in fact increasingly not only using, but dependent on it. These denials persisted through the early 2000s, though beyond 1998 or so it was largely only dead-enders maintaining this.
And from there it just continued to build. I'd argue that the linchpin argument wasn't money made selling Linux or Linux services, but companies based on it which simply couldn't exist by other means, of which the most notable early exemplar was almost certainly Google. Running its systems on proprietary Unix or Microsoft platforms would have been prohibitive in both cost and flexibility.