Even though I answered this on StackOverflow, I'll paste my solution here for completeness purposes:

Here's one way using split() hackery:

#!/usr/bin/perl

use strict;
use warnings;

my $f1 = 'file1.txt';
my $f2 = 'file2.txt';

my @pdb;

open my $pdb_file, '<', $f2
  or die "Can't open the PDB file $f2: $!";

while (my $line = <$pdb_file>){
    chomp $line;
    push @pdb, $line; 
}

close $pdb_file;

open my $shifts_file, '<', $f1
  or die "Can't open the SHIFTS file $f1: $!";

while (my $line = <$shifts_file>){

    chomp $line;

    my $pdb_line = shift @pdb;

    # - inner split: get the third element from the $pdb_line
    # - outer split: get the first element (character) from the
    #   result of the inner split

    my $criteria = (split('', (split('\s+', $pdb_line))[2]))[0];

    # - compare the 2nd element of the file1.txt line against
    #   the above split() operations

    if ((split('\s+', $line))[1] eq $criteria){
        print "$pdb_line\n";
    }
    else {
        print "**** >$pdb_line< doesn't match >$line<\n";
    }
}
[download]

Files:

file1.txt (note I changed line two to ensure a non-match worked):

1  H  35
1  A  22
1  H  20
[download]

file2.txt:

A  1 HB2 MET  1 
A  2 CA  MET  1
A  3 HA  MET  1
[download]

Output:

./app.pl
A  1 HB2 MET  1 
****>A  2 CA  MET  1< doesn't match >1  A  22<
A  3 HA  MET  1
[download]

-stevieb