It appears that both Libraries API and Variables API provide a function to retrieve the path to third-party library code installed under sites/all/libraries/.
From libraries.module, lines 9-22
<?php
/**
* Helper function to build paths to libraries.
*
* @param $name
* The machine name of a library to return the path for.
* @param $base_path
* Whether to prefix the resulting path with base_path().
*
* @return
* The path to the specified library.
*
* @ingroup libraries
*/
function libraries_get_path($name, $base_path = FALSE) {
?>From vars.module, lines 162-170
<?php
/**
* Returns the list of the directories where library files are looked in.
*
* @param $library
* The library to look for. This parameter will be used as directory name.
* @return
* An array of directories where the library can be found.
*/
public function getLibraryPath($library, $unused = array()) {
?>An issue where I suggested using the Libraries API module to move third-party code from the module directory to the libraries directory, and the module author opted to use the Variables API module to accomplish the same function:
#1007454: Rudimentary libraries support
I posted a support request issue against both projects, asking the respective maintainers to comment on this overlap of functionality and/or the possibility of consolidation. One module developer flatly refused to discuss the issue.

Comments
Aside from this one function,
Aside from this one function, these projects have completely different goals. The intent of the Similar Module Review group is for listing modules that have similar goals in an attempt to get the maintainers to work together to achieve those goals.
The issue queues are the best venue to discuss the specific function you are trying to resolve. Please do not cross-post content from existing issues for the sake of getting noticed.