No, they're not. They can run via CGI (so, yes, compiled for each request) but that's slow as ass. They run via Plack/PSGI - they can be deployed in a multitude of ways, including via FastCGI or running standalone using built-in webservers, or via Starman - the latter in particular is very fast indeed. With a simple "hello world" type app, > 6000 requests/sec can be easily handled. Obviously an app of more realistic complexity won't be quite that fast, but you'll still handle many requests every second with no trouble. http://stackoverflow.com/a/4770406/4040 contains some basic benchmarks.
EDIT: also, mod_perl is generally best avoided these days; it's old, not very pleasant to work with, and ties you to Apache. Writing an app with Dancer / Mojolicious etc means you can deploy in various different ways with ease.
I take it "they had it coming" is an implicit agreement that you are indeed trolling?
As whiskeyjack already said, if you believe there was code stolen, go ahead and prove it. The source repositories of both projects are publicly available, feel free to show examples of code that was "stolen".
If not, please do move along and stop tarring the image of the Mojolicious project and the Perl community at large with your senseless childish behaviour. The Perl community is better than this. We don't need in-fighting.
EDIT: also, mod_perl is generally best avoided these days; it's old, not very pleasant to work with, and ties you to Apache. Writing an app with Dancer / Mojolicious etc means you can deploy in various different ways with ease.