They're really two different things. Activestate is a win32 Perl distribution, while Cygwin is a unixy environment that happens to run Perl.

Cygwin is a bit more work to set up, but you get a lot more (bash, vim, gcc, etc). You can compile most XS modules straight from CPAN.

Activestate is easier to set up. It has its own package management system with precompiled binaries for the most common modules.

If all you need is "Perl on Windows", Activestate is probably your first choice. Of course, there's nothing stopping you from installing both.