File1:
>Seq1
ABCDEFGH
>Seq2
RNADIMSEQ
>Seq6
XYZ

File2:
>Seq3
ABCDEFGH
>Seq4
RNADIMSEQ

Output:
>Seq1  >Seq3
>Seq2  >Seq4
>Seq6  Not found

%hash=();
open(out, ">Output.txt");
open(sbjt, "File1.fasta") or die "File not found"; #Bigger file
$count =0;
while(<sbjt>)
    {
    chomp;
    if($_ =~ m/^w+/)
        {
            $hash{$previous} = $_  ;
            #print "$previousn";
        }
    else
        {
        $previous = $_;
        }
    $count++ ;
    }
    close sbjt;
    #print "$hash{$previous}";

%dash=();
$previous = undef;
open(query, "File2.fasta") or die "File not found"; #smaller
while(<query>)
    {
    chomp;
    if($_ =~ m/^w+/)
        {
            $dash{$previous} = $_  ;
            #print "$previousn";
        }
    else
        {
        $previous = $_;
        }
    }
    close query;

foreach $key (keys %dash)
{
         foreach $temp (keys %hash)
         {
            if($hash{$temp} eq $dash{$key})
            {
                push(@new_array, $temp);
            }
            next; #added
        }
        if(scalar @new_array>0)
        {
            print out "$keyt@new_arrayn";
        }
        else
        {
        print  out "$keytNot foundn";
        }
        @new_array=();
 }

 my $end_run = time();
my $run_time = $end_run - $start_run;
print "Job took $run_time secondsn";