FreeBSD is a nice environment, and I tend to gravitate to it (though I love Linux and Solaris as well). It does tend to work better in smaller environments than either Linux or Solaris.
There was recently a discussion of FreeBSD on the EeePC; it appears that while some items do not work (to be expected) it runs nicely and works nicely (including wireless). There was recently posted a simple introductory article which also refers to a comprehensive article on FreeBSD on the EeePC.
There was also an article (with followup) about running FreeBSD on the fitPC; in contrast to the EeePC, this sounds like it is not as good. However, the fitPC has less memory and a slower processor; it is unclear as to whether the processor is “fast enough” (I still use Pentium IIIs for my use!) or if it really is slow. It is, however, very surprising that the default Ubuntu install would be a graphical installation that swaps badly and comes without SSH.
The fitPC forums have a nice Linux on fitPC section, which also includes the BSDs as well. The biggest problem with FreeBSD seems to be its lack of a USB CDROM driver in the base kernel; however, apparently OpenBSD loads fine. Since the system has only 256M of memory, it perhaps should not be swamped with heavy desktop applications.