One minor difference is that splitting this way removes the close-paragraph, but not the open-paragraph, so you need to remove it.

my @arr = grep {/\[tab\]/ and s/^<p>//} split /<\/p>/, $contents;
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If you wanted to retain both tags, you could do so by splitting on a lookbehind expression:

my @arr = grep /\[tab\]/, split /(?<=<\/p>)/, $contents;
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You'd also retain the paragraph-close if you used it for $/ and read the string as a file.

{
  local $/ = '</p>';
  open (STR, '<', \$contents) or die "Opening string: $!\n";
  @arr = grep /^<p>/ && /\[tab\]/, <STR>;
  print "read $_\n" for @arr;
}
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But now I'm just getting silly.