If you want to compare those files line-by-line, you should lose the second while, i.e.

while (my $line2 = <FILE2>) {
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should just be

my $line2 = <FILE2>;
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and, of course, remove the closing brace from the second while block.

With your code as it is now, you're comparing: 34 with 28 (diff > 2); then 34 with 97 (diff > 2); then 98 with nothing! - you've read all of 2.txt by this point.

I'd also recommend you take a look at the syntax shown in the first two example statements in the documentation for open.