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I am unquestionably quite a bit biased on this topic. I wrote the CGI::Application module to solve exactly the problem you describe, so I have just a few opinions on the subject of run-mode management. :-)
IMHO, looking at the parameters in a template is ripe for failure. Unless you have a strict naming convention, I cannot imagine how you are going to assure that parameter names are not innocently reused for varying purposes from template to template. Looking at the name of the template is a LITTLE more sane. At least you have uniqueness -- unless you have some space-age file system which allows two files with the same name in the same directory. The idea of looking at the template name is really the functional equivalent of any "Server Page" system, in that regard. The only difference is that your code is not mixed in with HTML, as it usually is in ASP, JSP, Mason, EmbPerl or ColdFusion.
Not having code in a HTML an improvement, but there is still one HUGE problem in a server page architecture. Each template file (or "server page") represents a single screen, but it DOES NOT represent the ACTION which brough you to this screen! On the web, there is very often more than one way to get to a particular screen. Server page systems, including the system you’re describing, are incapable of cleanly implementing this behavior.
Consider a simple database application which allows an administrator to search, add, modify or delete an item. Imagine that your "search" function displays a list of matching results -- an "item list" screen. Also imagine that when you delete an item the user is returned to the item list screen.
Here are the functions of this hypothetical application, including the two we’ve mapped out:
As you can see, this application has only three screens, but it has SIX different actions which might be triggered. In a server page system you would have to put switch logic in each screen to figure out what to do:
Now, imagine a switch like this in every screen! And what do you do if you actually want to add a function, or change (for example) the "update" action to return to the "item detail" screen? You have to edit a spider web of files to make even the smallest change.
And the worst: Your code is now looking a lot like CGI "scripting" circa 1995!
CGI::Application allows you to decouple your screen ("pages", "templates", "states") from your actions ("run-modes", "transitions"). This means that you can cleanly share a screen between actions without having to write switch code to do so. Instead, you simply set up a "run-modes" dispatch table in an object-oriented Perl package which inherits from CGI::Application. Each mode maps to a Perl method, which in turn uses HTML::Template for output.
If you're interested in learning more about CGI::Application, I wrote an article about it:
Also, rob_au has offered a review of the module.