After reading both 'Beginning Perl' and 'Learning Perl', I can say, from a beginners perspective, that 'Beginning Perl' stands head and shoulders above the other. 'Learning Perl' assumes you have some prior knowledge of programming and if I had started with that book, I would have been completely lost by the 2nd chapter. Only because I read 'Beginning Perl' first was I able to make sense of 'Learning Perl'.
Also, the jokes in 'Learning Perl' are really quite lame and the constant references in the code to the Flintstones grows tiresome real quick. If they used realistic variable names and real case scenarios, plus back off a little on the attempt to be funny, it would be a good book to have. However, Jeff is correct when he mentions that they focus too much on the command line. If that's all you'll be writing for, then it will suffice.
But if you plan on writing for the web, download 'Beginning Perl'. You'll be glad you did. Not only is it free, but Simon Cozens is an excellent writer. I'm hoping that he'll release a new edition. If he does, I'll be first in line!