You can get by knowing one or the other well. Perl's advantages to me are the CPAN, the tooling culture, the testing culture, and a very pragmatic approach to getting things done without the language or ecosystem dictating how.
Python's advantages are slightly cleaner defaults in Python 3 and the fact that all code looks basically the same. (I'm not sure I see that as an advantage, but other people do.)
I think Perl and Python have a lot more in common than differences when it comes to what they are good at. If you know one scripting language, you don't gain as much when you learn the next. My recommendation is to learn something different, C, Haskell, Lisp or Prolog for example. That would make you think in different ways.
Also, chromatic (a Perl developer) gives a very balanced answer in a sibling to my answer, so I won't repeat what he said.
Among other things it overloads the basic operators, so $a+$b will do the right thing, even if $a and %b are matrices/images, so it is very easy to "read" if you are a perl person already.
Perl has its own strengths. In order to win as scripting language on the UNIX environment a language will have to get some things right very well. Two of them namely 'Processes' and 'Files(text)'. UNIX is really about these two things heavily. That is why you will see UNIX by a vanilla installation has shipped with tools like sed, grep, awk, cut, tr, cat and other text processing tools for decades. Because a file can act as a pretty good representation for data, storage and problem representation use cases. Another area that the language will have to get right is 'DBMs'.
Speaking of Perl's merits as scripting languages alone, Perl offers a native way of interacting with all these things that I mentioned in the previous paragraph. Things like ``, system(), open(), close() , die(), chomp, while<FILEHANDLE>), split(), grep, !~ , ~= and regular expressions make text processing a breeze. In addition, Higher order parsing is very easy in Perl too, Regular expressions are first class objects. For more information on this you can read Mark Jason Dominus's Higher order Perl. Which is a free book.
Now coming to Perl's merits as general purpose scripting language. You have your usual language tool kit with data structures(usual numbers, strings), arrays, hashes. Flow control, functions, OO, functional programming features. But the plus and the biggest winner is the extension system. There is a huge repository of readily solved problems on the CPAN. You have language extension modules like Moose, Try::Tiny, etc etc.
In terms of the web development ecosystem, Perl has catalyst, DBIx::Class, Plack etc etc. You also have a good asynchronous programming framework.
In terms of documentation. Check out the amazing perldoc.perl.org. There is also Learning Perl, Programming Perl and recently Chromatic's beautiful book 'Modern Perl book'.
In terms of development practice and stability. Perl has a track record and battle tested for decades now, Its used to develop mission critical applications. For best practices you can read Damian Conway's Best practices book.
Also, Checkout enlightened Perl and Task::Kensho for the best of the breed modules.
As a plus and cherry on the cake, there is a new sister programming language called Perl 6 in the making. With great concepts, cleaner defaults and more pragmatic in the real world.
Perl 6 is usable today with Rakudo. Give it a whirl.
I would prefer to use Perl over bash/awk/sed since Perl is good at the same things and more and has alot more libraries.
Python is basically Perl but with different syntax, libraries, and community.
Perl has an emphasis on libraries. CPAN is the gold standard for the scripting languages. (To see what I mean -- search for signatures, Moose and Acme::Bleach on search.cpan.org. (+) )
Another good thing is the community of smart and laid back people.
I personally prefer to do Perl because it is fun.
The main disadvantage with the Perl "everything and the kitchen sink" attitude is if you are in a group without good coding standards... Perl also gets a tougher learning curve in the beginning, just from there being more to learn.
(+) Joke modules on CPAN generally start with Acme.
Edit: Huh, why down votes? Just a reflex by language trollers? :-)