Perl is Perl so scripts written in Perl will run with Activestate, Strawberry and/or any *nix version*.
I moved TO Strawberry from Activestate about 5 years ago because Strawberry comes with a C-compiler (gcc) and therefore - in my experience - has the ability to run more CPAN XS modules than Activestate. I found Activestate's autobuild process lacking and not all PPM's were available. It was much easier to just go to CPAN like I do on every other version of Perl.
"the Perl Scripts running in production environment use Activestate" statement I'm assuming means that Activestate is the Perl that is loaded on the production machines to run the scripts. There is no reason those scripts can't run on a Strawberry Perl installation or vice versa (your scripts run on an Activestate distribution).
*For the most part, excluding things like Win32::<Modules> on *nix.