Like others already wrote, in short:
shared project
reuse on the code (file) level, allowing for folder structure and resources as well
pcl
reuse on the assembly level
What was mostly missing from answers here for me is the info on reduced functionality available in a PCL: as an example you have limited file operations (I was missing a lot of File.IO fuctionality in a Xamarin cross-platform project).
In more detail
shared project:
+ Can use #if when targeting multiple platforms (e. g. Xamarin iOS, Android, WinPhone)
+ All framework functionality available for each target project (though has to be conditionally compiled)
o Integrates at compile time
- Slightly larger size of resulting assemblies
- Needs Visual Studio 2013 Update 2 or higher
pcl:
+ generates a shared assembly
+ usable with older versions of Visual Studio (pre-2013 Update 2)
o dynamically linked
- lmited functionality (subset of all projects it is being referenced by)
If you have the choice, I would recommend going for shared project, it is generally more flexible and more powerful. If you know your requirements in advance and a PCL can fulfill them, you might go that route as well. PCL also enforces clearer separation by not allowing you to write platform-specific code (which might not be a good choice to be put into a shared assembly in the first place).
Main focus of both is when you target multiple platforms, else you would normally use just an ordinary library/dll project.