I'm not at all familiar with the inner workings of the UNIX file systems, as in how the bits and bytes are stored, but really that part is interchangeable (ext3, reiserfs, etc).
When people say that UNIX file systems are better, they might mean to be saying, "Oh ext3 stores bits in such as way that corruption happens way less than NTFS", but they might also be talking about design choices made at the common layer above. They might be referring to how the path of the file does not necessarily correspond to any particular device. For example, if you move your program files to a second disk, you probably have to refer to them as "D:\Program Files", while in UNIX /usr/bin could be a hard drive, a network drive, a CD ROM, or RAM.
Another possibility is that people are using "file system" to mean the organization of paths. Like, for instance, how Windows generally likes programs in "C:\Program Files\CompanyName\AppName" while a particular UNIX distribution might put most of them in /usr/local/bin. In the later case, you can access much more of your system readily from the command line with a much smaller PATH variable.
Also, since you mentioned grep, if all the source code for system libraries such as the kernel and libc is stored in /usr/local/src, doing a recursive grep for a particular error message coming from the guts of some system library is much simpler than if things were laid out as /usr/local/library-name/[bin|src|doc|etc]. If you already have an inkling of where you're searching, though, cygwin grep performs quite well under Windows. In fact, I find for full-text searching I get better results from grep than the search facilities built into Windows!