Why does Path Finder show less available disk space, compared to Finder?
Firstly, Finder and Path Finder may be using different bases for file size calculation. You can switch between Base 10 and Base 2 in Preferences > Browser.
You can see the difference between the two by running the following in the command line:
df -H /
df -h /
Secondly, it's known that Finder doesn't take into account Time Machine snapshots.
If you navigate to About This Mac > More Info > Storage, you'll see that the space that Finder is not taking into account, when doing calculations, belongs to the snapshots.
You can use Disk Utility for more detailed information on hard drive capacity, available and used space.