I've also got Strawberry Perl installed on this box, but no other perls beyond these two. So far, they've never had any conflicts, as far as I was able to tell; invoking perl from a Cygwin shell always gives me Cygwin's perl, invoking it from a DOS command line alwasy gives me Strawberry.
I've got a slightly different Perl version, though:
$ perl -v
This is perl 5, version 14, subversion 2 (v5.14.2) built for cygwin-th
+read-multi-64int
(with 7 registered patches, see perl -V for more detail)
Copyright 1987-2011, Larry Wall
Perl may be copied only under the terms of either the Artistic License
+ or the
GNU General Public License, which may be found in the Perl 5 source ki
+t.
Complete documentation for Perl, including FAQ lists, should be found
+on
this system using "man perl" or "perldoc perl". If you have access to
+ the
Internet, point your browser at http://www.perl.org/, the Perl Home Pa
+ge.
$
As far as I can tell, this is because I'm using a 32-bit Cygwin (corroborated by the fact that the Cygwin installer is also offering me 5.10.1 and 5.18.2), rather than a 64-bit one. I don't know if this should make a difference, but I couldn't help but notice.