There are some efficincies to be had in the general approach. It is unclear if you want [ [1], [2] ] to be equal to [ [1,2] ]. Regardless the earlier you can fail the better for speed:

my $ha = [[1,2],
       [5,5,5],
       [1,2,],
       [3,4]];

my $hb = [[4,3],
       [1,2],
       [2,1,1],
       [5,5,5]];
      
# flatten
my @ha = map{ @$_ } @$ha;
my @hb = map{ @$_ } @$hb;

# fail immediately unless equal num elements.
if ( @ha != @hb ) { 
    print "Not equal num items!\n";
}
else {
     # now no choice but to sort or do detail compare
     if ( (join ' ', sort @ha) eq (join ' ', sort @hb) ) {  print "Equ
+al\n" }
     else { print "Not equal\n" }
}
[download]

It is possible to use a hash to avoid the sort, even with duplicate values simply by counting occurences as implemented by BrowserUk