Some Pros/Cons off the top of my head:

ActivePerl

• Pro: Quick and easy to install. Corproate friendly because it comes in Microsoft Installer format.
• Pro: Comes with Windows specific modules so much better suited for Windows specific developement.
• Pro: Can integrate with Windows Scripting Host (WSH) and IIS. And the .pl extension can be associated with perl.exe.
• Pro: ActiveState provides additional modules in PPM format. Think of them as binary distributions of the modules. These can easly be downloaded using the PPM tool that comes with ActivePerl.
• Con: Harder to add modules that are not in PPM format since Windows does not come with a Make utility or a compiler. I think Microsft's make utiltiy is nmake.exe and you can probably track that down fairly easily so adding pure Perl modules should not be too difficult. However, adding ones with C code will be a lot harder.

For Cygwin, you get a UNIX like environment which makes cross-platform development easier and since it comes with GCC it is a lot easer to install additional Perl modules.

Also, I have not seen any benchmarks, but since Cygwin adds an extra abstraction layer I would expect ActivePerl to outperform it if performance really matters to you.

Of course, there's nothing to preclude you from installing both....

Update: fixed several typos.