If you have no control over your XML format and you are stuck using XML::Parser, then you can igonre the rest of this post. Otherwise, please consider the following.

While I'm sure what you have is valid XML, it's too bad it isn't structured differently. Had your CustomDimensionName and customBucketValueString elements been children of customBucket, you could have filtered your information as follows:

use strict;
use warnings;
use XML::Twig;

my $xmlStr = <<XML;
<foo>
    <customBucket>      
        <customDimensionName>Strategy</customDimensionName>
        <customBucketValueString>Test1</customBucketValueString>
    </customBucket>
    <customBucket>
        <customDimensionName>SubStrategy</customDimensionName>
        <customBucketValueString>Test2</customBucketValueString>
    </customBucket>
</foo>
XML

my $t = XML::Twig->new();
$t->parse($xmlStr);
for my $bucket ($t->root()->children('customBucket')) {
    if ($bucket->first_child('customDimensionName')->text() ne 'Strate
+gy') {
        print 'customDimensionName '    , $bucket->first_child('custom
+DimensionName'    )->text(), "\n";
        print 'customBucketValueString ', $bucket->first_child('custom
+BucketValueString')->text(), "\n";
    }
}

__END__
customDimensionName SubStrategy
customBucketValueString Test2
[download]

I abandoned using XML::Parser once I discovered XML::Twig, which I find to be easier to understand and use.