Actually that is a lot simpler to solve assuming one "element" per line:

use warnings;
use strict;

while (my $line = <DATA>) {
  # Assume one "element" per line
  if ($line =~ /<(\w+)>(.*?)<\/\1>/) {
    (my $midstr = $2) =~ tr/<>/[]/;
    $line = "<$1>$midstr</$1>\n";
  }
  print $line;
}

__DATA__

<sometag> my data here </sometag>
<anothertag> further text </anothertag>
<furthertag> not good as contains <this> in angle brackets </furtherta
+g>
<byetag> another possibility is <more> <than> one <angle pairs> in her
+e </byetag>
[download]

Prints:

<sometag> my data here </sometag>
<anothertag> further text </anothertag>
<furthertag> not good as contains [this] in angle brackets </furtherta
+g>
<byetag> another possibility is [more] [than] one [angle pairs] in her
+e </byetag>
[download]