If I understand your problem correctly, you want to create multiple Android apps that are similar to one another (i.e., have a lot of the same source code), but which are different in particular (minor) ways, and you want each of these apps to have a distinct package, so that it can be separately uploaded and distributed on an app store such as Google Play. A Project Library is an excellent facility for accomplishing those goals.
I'm assuming that the differences between your various versions are minor, involving things like resources and the app name and package, and a switch that turns on certain features for a paid version while leaving them off for a free version.
Even if that is not the case, by using polymorphism in the ways described below, your various apps could differ in significant ways and still share a common Project Library.
A Project Library can be defined in Eclipse in the same way as any Android project can be defined, but it is marked as a Project Library (by checking the "Is Library" box near the bottom of the Android page of the library's Project Properties dialog) and cannot be compiled and run on its own. Instead, it is intended to be included by reference in one or more other projects which are actual apps (by adding a reference to it on the Android page of each such app's Project Properties dialog). These apps will use the Project Library, and thus will share its code and capabilities.
Each such referencing app will have its own manifest file (where their respective, different packages can be declared), and they can also define their own classes (including classes derived from the Activity and/or Application classes of the Project Library), so that these classes can be specialized polymorphically for each app that uses the Project Library (e.g., by overriding methods or by providing definitions for methods that are defined as abstract within the Project Library's Activity- or Application-derived classes), although you can also use those Library classes without modification (provided that they are not abstract) by simply referencing them within the manifest file (e.g., in an activity or application tag) of each app that uses the Library, just as you would reference Activity or Application-derived classes defined within the app itself.
If you decided to use this approach, then you would put your main source files in a Project Library, and would create a separate project for each app you want to produce, each of which would reference the Project Library. The manifest file of the Project Library would be overridden by the manifest of whatever project is being created using that Library (actually, I think that the Project Library's own manifest is completely ignored, not just overridden, but nonetheless it is useful to create a manifest for the Library, so that you can manually template - copy and edit - the manifest of each project that uses it from the Library's own manifest).
I have used this approach to create multiple android apps that share some of the same capabilities, and it has worked very well for me.
Regarding package naming, any old package name will work for a library project, but of course it makes sense to use the same prefix for the Library Project's package as you use for your various individual (e.g., free vs. paid) apps that use it, with something like ".library" as the last part of the name, while the various apps could have endings like ".myappfree" and ".myapppaid". Naturally, you would want to use your reverse domain name convention for the library's package prefix to prevent conflicts, just as you would for a package name of a released app.
In Windows, a nice, open-source tool for comparing code bases is WinMerge:
http://winmerge.org/
If I were in your position, however, I would only use this tool to manually identify differences, and would not attempt to use it to automate the refactoring of your code into a Library Project. That would be best done under your own (manual) control.
Finally, as an alternative, you might consider using a single app that is free and that has your free app's capabilities by default, with an option to upgrade to your full app's capabilities (delivered within the same APK) via an in-app payment, rather than having separate free and paid apps. In-app payments have improved a great deal in the past several months (with the release of version 3 of IAB), and although there are still some glitches, they have become a more practical alternative to the free/full dichotomy than they were at first.
