All Linux distros are roughly equal. What one can do, any other distro can do.
That's the nice thing about open source software. Any improvements that get made in one distro can instantly be translated to another one.
That being said what I like is the ability to use advanced package managers like Apt and Yum. These are programs that allow you to download/install programs and updates over the internet.
One of the major hassles with software in Linux is dependances. The idea is that you create functionality in one program or software library that can be used in other programs. So say you download the GTK+ libraries and that can be used by another program to create GUI widgets (the little things like the maximize minimize buttons and standard menus and interfaces). So that way the author of the program can concitrate on the basic functionality of the program rather then wasting his/her time redoing the GUI portion from the low-level up.
So it makes it easier and cheaper to make programs. The downside is that a user has to have GTK+ pre-installed to use that program.
Stuff like that is called "dependancies". In Windows when you install programs your either using the standard Win32 API (the standard set of libraries (*.dll files) and programs in all Windows OSes from Win95 up) or all the third party dependancies are installed along with the program from the installation media.
Linux programs don't do this and expect you to get all the dependancies yourself. They'll tell you in the docs sometimes what to do, but it's up to you to do it.
If you have lots of missing dependancies or version conflicts it can be a big pain. This is called "dependancy hell" and is a major hurdle for new Linux users, next to getting badly supported hardware working properly (such as nvidia motherboards or ATI video cards).
Apt and Yum solve dependancy hell by keeping track of programs and libraries in online repositories. By updating against these repositories you keep your OS patched and up to date, and when you use apt or yum to install programs all the dependancies are pre-calculated and are downloaded/updated/installed in your computer as you need them.
So say to install mplayer you would go "apt-get install mplayer" and it would look for packages that match that name, check out the dependancies and then download the program and all the dependancies and install them and set them up with a initial default configuration. This make things easily.
Or for instance you have a serious security flaw in your OS. So the developers will issue a patch, the package maintainers will create a updated package. Then all you have to do is:
apt-get update
apt-get upgrade
And it'll get fixed. Using yum you would go :
yum update
The 3 distros that do this very well are Debian, Gentoo, and Fedora.
Out of those Fedora is probably the easiest for a Windows user to relate too. Easy graphical installer, and a vast user base. Yum is installed by default and Apt is optional but supported. However the initial packages are limited in scope. Several programs are not normally aviable by the official Fedora sources and you have to rely on third party repositories for many programs. Luckly those third party repositories are of decent quality. Fedora, like all Redhat based distros (like Suse/Mandrake) use RPM packages and have adapted Yum from Yellowdog (powerPC linux) and apt-get from Debian for their distro.
People find Gentoo very satisfing though, since it's minimallist installing approach means that you do everything by hand and people learn a lot from doing this for the first time. However everything is compiled from scratch (optionally) and it can take several hours to complete a full install. Even a day or 2. They have a optional binary install. Gentoo is going to be the most atractive for the "advanced tweaker". Since everything is compiled from source it offers you the most options aviable and many people spend hours figuring out the optimal configuration and compile options for their system. It is based on the portage package management system. The gentoo forums are a great help for many people and offers many learning opertunities.
Debian is commonly used by advanced users and has the best quality packages, however going from Windows to Debian is a very big change and is difficult for many people to adjust. Debian is going to have the highest quality packages aviable for it. Very professional very serious. Some people get tired of the politics and whatnot, but they are hardcore on their positions about free software and legalities.
Out of those Fedora is going to be most "user friendly". However reviews online tend to be slightly negative. Other "user-friendly" style distros are Suse and Mandrake and many people prefer those over Fedora, especially for the newbie. However I feel that their official support of Yum and Apt more then make up for it's deficiencies. Third party repositories include Dag, ATrpms, Freshrpms, but those are not recommended by Fedora to use because they don't cooridant officially with the official repositories. "At your own risk" sort of thing.
I use Fedora and Debian. However if you want maximum tweakatude go Gentoo. However using Linux is a very abrupt change from Windows. Very different enviroments. The nice thing though is that once you get used to the Unix way of doing things then your can easily adapt to a whole host of other operating enviroments such as the BSDs, OS X (as a "hacker" type), Solaris, etc etc.
Check out the docs at
www.tldp.org and especially the bash introduction guide, and the Linux administrator guide as they are distro agnostic, anything you learn their can be easily used in any distro and most unixes. Which is nice since you don't have to worry about getting stuck to any single distro.