Java and a few java libraries provide a "classpath" exception. To me, this seems similar to the LGPL's linking exceptions. What is the difference between the GPL with a classpath exception and the LGPL?
The LGPL and GPL + the Classpath exception share the property that if you link code under these terms into your program, the resulting derivative work does not have to be made available as free software. Instead you can copy and distribute the resulting binary executable under terms of your choice. This means that the source code does not have to be provided to downstream recipients.
However, the LGPL 2.1 says (sec. 6):
As an exception to the Sections above, you may also combine or link a "work that uses the Library" with the Library to produce a work containing portions of the Library, and distribute that work under terms of your choice, provided that the terms permit modification of the work for the customer's own use and reverse engineering for debugging such modifications.
While LGPL 3 says (sec. 4):
You may convey a Combined Work under terms of your choice that, taken together, effectively do not restrict modification of the portions of the Library contained in the Combined Work and reverse engineering for debugging such modifications, if you also do each of the following: [...]
I.e.: the LGPL permit modifications of the combined work and reverse engineering for debugging such modifications.
That is not much freedom, but apparently some people did not like the explicit permission to do modify the work and to make use of reverse engineering, so GPL + the Classpath exception does not contain such a permission.