The purpose is to save lots of traffic.
The Linux tarball is around 75MB, whereas the patches usually just have a few KB.
So if you compile your own kernel, and update to each new minor version the day it is released, instead of redownloading a new 75MB tarball for each minor update, you just download (for example) the main tarball for a given version once and then the patch for the version you actually want. When there is an update you re-use the already downloaded main tarball.
linux-3.14.tar.xz + patch-3.14.{1..n}.xz is below 100MB in total.
linux-3.14.tar.xz + linux-3.14.{1..n}.tar.xz is several times 100MB.
There is no downside to patching, the final result is identical, unless you do something wrong.
In Debian terminology, when you run
apt-get source linux-image-3.19.0-trunk-amd64
(or the equivalent apt-get source linux), you're actually downloading and extracting the source package. This contains the upstream code (the kernel source code downloaded from kernel.org) and all the Debian packaging, including patches added to the kernel by the Debian kernel team.
When you run
apt-get install linux-source-3.19
you're actualling installing a binary package which happens to contain the source code of the Linux kernel with the Debian patches applied and none of the Debian packaging infrastructure.
The source package's name is just linux; apt-get source will convert any binary package name it is given into the corresponding source package name.
By the way, since experimental packages aren't upgraded automatically, you should make sure you've updated your copy of linux-source-3.19 and re-extracted it before comparing; the .dts file you're seeing in your diff was introduced in the latest update. The packages currently in the archive all contain this file.
The remaining differences are pretty much normal: as has been indicated in the comments, debian contains all the packaging and is only in the source package, .pc is used by quilt to keep track of the original files modified by patches, and is also only in the source package, and the .1 files are generated manpages, probably a side-effect of the kernel build, and therefore only appear in the binary package (but they shouldn't really be there).
The reference package is the source package, as obtained by apt-get source. This builds all the kernel binary packages, including linux-source-3.19 which you install with apt-get install. The latter is provided as a convenience for other packages which may need the kernel source; it's guaranteed to be in the same place all the time, unlike the source package which is just downloaded in the current directory at the time apt-get source is run.
As far as documentation goes, I'd follow the Debian documentation in the kernel handbook (section 4.5). Rebuilding the full Debian kernel as documented in section 4.2 which you linked to takes a very long time because it builds a number of variants.
Best Answer
Well, first off, you speak of BSD as if they're is only one. Technically, I suppose, there is the original one they were all derived from—last release was in 1995. Searching for "4.4-Lite2" finds several copies, you can find out more about it at the Wikipedia's Berkeley Software Distribution article.
Derived from it are—among many things*—FreeBSD, OpenBSD, and NetBSD. All three are open source, and you can get their source code. Someone who says BSD nowadays is probably referring to one of them.
If you want to quickly browse them, there is a FreeBSD and Linux Kernel Cross-Reference. That site also has several other Unix-like kernels.
Unlike Linux, however, which exists as a standalone kernel project, the BSD kernels often are part of a larger project—they aren't independent of the distro. For example, the FreeBSD kernel is part of the FreeBSD project and is maintained in the same subversion repository as the rest of the distro.
There are some places the kernel is used without the rest of the userland, e.g., in Debian's kFreeBSD port.
*: Parts of the original BSD have gone pretty far indeed. For example, you'll see the notes about portions of software being copyright The Regents of the University of California all over the place. A lot of that is BSD. If you read the many-page notice included with Windows, for example, it's there.