First, a bit of background so you know where I'm coming from: I'm the original author of the new Test::Harness module, I'm heavily involved in the Perl-QA community, I teach people testing, I have several testing modules on the CPAN and have written and published the results of Test Survey Results. In short, I know this area very, very well, so I hope you'll understand that I don't say "don't use PerlUnit" out of complete ignorance.

PerlUnit was an interesting project, but it's a dead one. Also, it does not integrate with the standard Perl testing tools. As a result, the wealth of powerful testing modules in Perl are pretty much not an option for you. Out of over 15,000 distributions on the CPAN, it appears that only 14 of them use PerlUnit (its front-end is named Test-Unit) and half of those are for one author on one set of related modules.

As for what people are actually using, I ran an analysis of the testing software used in CPAN modules and the top ten (out of 287) testing modules identified were:

 Module          Number of test programs
 Test::More                        44461
 Test                               8937
 Test::Exception                    1379
 Test::Simple                        731
 Test::Base                          316
 Test::Builder::Tester               193
 Test::NoWarnings                    174
 Test::Differences                   146
 Test::MockObject                    139
 Test::Deep                          127
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Aside from Test, a legacy module used by older code, the standard Test::Harness based testing modules (Test::More, Test::Exception, Test::Differences, etc.) will be far more useful for you and new testing tools are coming out all of the time for it.

Of course, if the customer is requesting PerlUnit because they rely heavily on it, you may be stuck, but try to avoid it. If it's being considered because of its xUnit philosophy, I recommend you check out Test::Class. It's a great module and I use it all the time.