First, I would use ForceArray on the moreSpecific tag (if there is only one 'moreSpecific' node, it will not make an array), and you don't need the count to access all of the subnodes.

my $morelist = $content->{'soapenv:Body'}{'getKeywordVariationsRespons
+e'}{'getKeywordVariationsReturn'}{'moreSpecific'};

for my $more (@$morelist) {
  print "$more->{text}\n";
  print "$more->{advertiserCompetitionScale}\n";
  print "$more->{searchVolumeScale}\n";
  $more->{more} = $more->{text};
  $more->{comp} = $more->{advertiserCompetitionScale};
  $more->{pop} = $more->{searchVolumeScale};
}
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Update: fixed, updated example.