Yeah, Gentoo is easier to deal with one you get the hang of it
"Ease of use" is highly subjective and depends a lot on what do you consider "easy" and what do you consider "use". But I am not going to spoil the thread with my dissertations about that because I think that will not help WillingToLikeLinux
to understand anything about the topic at hand.
To the topic at hand: a binary distro is formed by packages that have been pre-compiled, in a similar way to other OSes, where you pick a binary package and just install it and start using it. This is usual for example in Windows (just to name a well known example), where most users don't even have a compiler installed unless they are programming or developing something, but it's true also for most linuxes and most other OSes in general. Because these binaries must run in a wide range of hardware, they are compiled with generic enough defaults, that grant that the same binary file will run on, let's say, a pentium 4, an amd k8 or a core2 cpu, and they are also compiled with all the features enabled by default.
On the contrary, on a source based distro, you start with the source code of the programs, in whatever language they are written (C, perl, mono, whatever), and they are compiled from scratch, and then installed to your system. This takes much longer, and gives as a result a distribution that's tailored to your needs. You can choose to compile code that's specific for a k8, and that will be incompatible with any cpu that doesn't support all the sub-sets of instructions that the k8 cpu's do. You can also decide to disable gtk or gnome support in your applications if you are only going to use console or kde. Someone could argue that having support for both ncurses and slang in the same program is a waste, because they both do the same thing, so you can disable one of them. Someone could argue that having support for 6 database types in php is silly because you are using just mysql or postgresql, then you can disable the others. The results will be a smaller footprint, and less code to deal with (which specially in server stuff like php or apache can limit the number of potential bugs that a server will expose at a given time).
An advantage of source based distros is that it's a bit easier to roll your own when you need to patch a given package (you already have the sources, and the toolchain is there by default since it's needed by the OS). However some others will argue that having a compiler installed on a server can be problematic (that can be easily solved by compiling the package into another machine though).
Gentoo in that regard is very configurable and easy to manage when compared to LFS for example. It has a proper package manager that lets you disable and enable features (USE flags) and that adjust all the dependencies according to that, which is in my opinion the best thing about it, save the community and the documentation which is certainly good as well.