It may help to use objects instead of explicit hashes. The hashes are still effectively there and the nested structure is still effectively there, but you can provide methods that give friendly ways of managing the data that hide the underlying complexity. Consider:

#!/usr/bin/perl
use strict;
use warnings;

package SNP;

sub new {
    my ($class, %params) = @_;

    die "id parameter required by $class constructor\n" if !exists $pa
+rams{id};

    $params{genes} ||= {};

    return bless \%params, $class;
}


sub addGene {
    my ($self, $geneId, %params) = @_;

    $self->{genes}{$geneId} ||= Gene->new(id => $geneId, %params);
    return $self->{genes}{$geneId};
}


sub match {
    my ($self, $other) = @_;
    my @otherGenes = sort keys %{$other->{genes}};
    my @genes      = sort keys %{$self->{genes}};
    my $result     = '';

    return "$self->{id} and $other->{id} differ in number of genes.\n"
        if @otherGenes != @genes;    # different number of transcripts

    # Check all genes match
    for my $gene (@genes) {
        my $matchFail = $self->{genes}{$gene}->match($other->{genes}{$
+gene});

        next if !$matchFail;
        $result .= "- Gene mismatch for $gene:\n";
        $result .= $matchFail;
    }

    if ($result) {
        $result = "$self->{id} does not match $other->{id}:\n" . $resu
+lt;
    }

    return $result;
}


package Gene;

sub new {
    my ($class, %params) = @_;

    die "id parameter required by $class constructor\n" if !exists $pa
+rams{id};

    $params{trans} ||= {};
    return bless \%params, $class;
}


sub addTranscript {
    my ($self, $transId, %params) = @_;

    $self->{trans}{$transId} ||= Transcript->new(id => $transId, %para
+ms);
    return $self->{trans}{$transId};
}


sub match {
    my ($self, $other) = @_;
    my @otherTrans = sort keys %{$other->{trans}};
    my @trans      = sort keys %{$self->{trans}};
    my $result     = '';

    return "$self->{id} and $other->{id} differ in number of transacti
+ons\n"
        if @otherTrans != @trans;    # different number of transcripts

    # Check all transcripts match
    for my $transName (@trans) {
        my $matchFail =
            $self->{trans}{$transName}->match($other->{trans}{$transNa
+me});

        next if !$matchFail;
        $result .= "-- Transcript mismatch for $transName:\n";
        $result .= $matchFail;
    }

    return $result;
}


package Transcript;

sub new {
    my ($class, %params) = @_;

    die "id parameter required by $class constructor\n" if !exists $pa
+rams{id};

    $params{props} ||= {};
    return bless \%params, $class;
}


sub setProp {
    my ($self, $prop, $value) = @_;

    $self->{props}{$prop} = $value;
}


sub match {
    my ($self, $other) = @_;
    my @otherProps = sort keys %{$other->{props}};
    my @props      = sort keys %{$self->{props}};
    my $result     = '';

    return if @otherProps != @props;    # different number of properti
+es

    # Check all properties match
    for my $propName (@props) {
        if (!defined $other->{props}{$propName}) {
            $result .= "$self->{id} has $propName but $other->{id} doe
+sn't\n";
            next;
        }

        if ($self->{props}{$propName} ne $other->{props}{$propName}) {
            $result .=
                "--- $self->{id} and $other->{id} property $propName d
+iffers:\n";
            $result .=
                "    '$self->{props}{$propName}' and '$other->{props}{
+$propName}'\n";
            next;
        }
    }

    return $result;
}


package main;

my $snp1  = SNP->new(id => 'SNP1');
my $gene  = $snp1->addGene('Gene1');
my $trans = $gene->addTranscript('Trans1');

$trans->setProp(big   => 1);
$trans->setProp(color => 'blue');
$gene  = $snp1->addGene('Gene2');
$trans = $gene->addTranscript('Trans2');
$trans->setProp(big   => 1);
$trans->setProp(color => 'green');

my $snp2 = SNP->new(id => 'SNP2');
$gene  = $snp2->addGene('Gene1');
$trans = $gene->addTranscript('Trans1');

$trans->setProp(big   => 1);
$trans->setProp(color => 'blue');
$gene  = $snp2->addGene('Gene2');
$trans = $gene->addTranscript('Trans2');
$trans->setProp(big   => 1);
$trans->setProp(color => 'blue');

print $snp1->match($snp2);
[download]

Prints:

SNP1 does not match SNP2:
- Gene mismatch for Gene2:
-- Transcript mismatch for Trans2:
--- Trans2 and Trans2 property color differs:
    'green' and 'blue'
[download]