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If you have it deployed somewhere, what is your setup like, and what kind of performance are you getting out of it? Do you feel like the development process was any faster than other methods (old-school plain CGI.pm, CGI::Application, etc), or just a better/different way to organize the code on the site? Have you had trouble finding the answers to your Catalyst and related module questions (I've run into a few things that were hard to figure out on my own)?
So I've read the two main books written on Catalyst (The Definitive Guide to Catalyst... is MUCH better) and done lots of digging in the CPAN docs, and I have to say, for me, the learning curve was definitely a few months of on-and-off playing around with it. It wasn't the object orientedness of it all so much as you feel like to do things right, you might have to learn 3 or 4 (or 5...) new programs/skills.
For instance, not only are you learning about Catalyst, you might also want to start using DBIx::Class (I was used to DBIC::MySQL, etc), Template::Toolkit (HTML::Template was my old standby), one of the form generation modules (FormBuilder, etc), plus all of the other plugin goodness. I found that in the beginning, even though I was following the examples online and in the books, I had to do a lot of digging to figure out how to do things I knew how to do with other modules. Search engines are definitely your friends with Catalyst.
But after all that, it finally starts to click and things fall into place. For me, what really kicked things off was just starting to build a site with all of the above. Having something concrete to build with a goal in mind was a great learning tool, plus once you figure out how to do something new/tricky, you then have a reference you (should) understand easily later.
All in all, I think I'll try to stick with Catalyst for future large sites I build. CGI::Application worked well for me for many years, but Catalyst just seems so much more flexible and powerful, if not faster to develop in.