my %rehash;
for my $SUBNAME (sort keys %HoH){
  for my $testname (sort keys %{ $HoH{$SUBNAME}  })  {
    for my $value_name (sort keys %{  $HoH{$SUBNAME}{$testname} } ){
     my $val =  $HoH{$SUBNAME}{$testname}{$value_name};
     if (exists  $rehash{$testname}{$value_name}
         and      $rehash{$testname}{$value_name}[1] > $val){
       # Do not update - greater value exists
     }else{
       $rehash{$testname}{$value_name} = [$SUBNAME,  $val];
     }
    } 
  }
}


for my $testname (sort keys %rehash){
   print "For $testname:\n";
   for my $value_name(sort keys %{ $rehash{$testname} }){
     print "   $rehash{$testname}{$value_name}[0] has $value_name\=$re
+hash{$testname}{$value_name}[1]\n";
  }
}
[download]

Thanks for the update!
I have updated the example with few more values. How to display the first 2 (or more) results not just the biggest value and how to sort by first value1 and add value2 as a pair?
I suppose the values must be added to an array, sorted then display first, second, third etc. element of that array. Hash of hashes or hash of arrays are still unclear for me.

__OUTPUT__
For Test1
   SUB2 has value1=2800 and value2=0.05
   SUB3 has value1=2700 and value2=0.25
For Test2
   SUB2...
   SUB3...

etc.
[download]

Since you did not specify it, I assume you want the comparison done on "value1" only. Based on that, here is the code:

my %rehash;
for my $SUBNAME (sort keys %HoH){
  for my $testname (sort keys %{ $HoH{$SUBNAME}  })  {
     my $val =  $HoH{$SUBNAME}{$testname}{value1};
     if (exists  $rehash{$testname}{$SUBNAME}{value1}
         and     $rehash{$testname}{$SUBNAME}{value1} > $val){
       # Do not update - greater value exists
     }else{
       $rehash{$testname}{$SUBNAME} = $HoH{$SUBNAME}{$testname};
     }
  }
}


for my $testname (sort keys %rehash){
   print "For $testname:\n";
   for my $SUBNAME(sort keys %{ $rehash{$testname} }){
     print "   $SUBNAME has " 
       , map( {" $_=$rehash{$testname}{$SUBNAME}{$_};"} sort keys %{$r
+ehash{$testname}{$SUBNAME}}),
       ,"\n";
  }
}
__OUTPUT__
For Test1:
   SUB1 has  value1=2300; value2=0.01;
   SUB2 has  value1=2800; value2=0.05;
   SUB3 has  value1=2700; value2=0.25;
For Test2:
   SUB1 has  value1=5000; value2=0.34;
   SUB2 has  value1=5500; value2=0.34;
   SUB3 has  value1=5800; value2=0.45;
For Test3:
   SUB1 has  value1=3000; value2=0.10;
For Test4:
   SUB1 has  value1=7000; value2=0.33;
[download]

At this point, your original problem has been long solved, so please make further enhancements yourself.

             I hope life isn't a big joke, because I don't get it.
                   -SNL