I can confirm your results on AS 5.10; and (maybe) point out that it does not appear to be conflict between the regexes as I get similar disparate results using tr to count the newlines:

use Data::Dump qw{dump};

$data = do { local $/ = undef; <DATA> };

# in single call
dump [
        scalar( $data =~ tr[\n][\n] ),
        scalar($data =~ s/\n/\n/g),
        scalar($data =~ s/(\w+)/\1/g),
        length($data)
];

# in multiple calls
dump [  scalar( $data =~ tr[\n][\n] ) ];
dump [  scalar($data =~ s/\n/\n/g) ];
dump [  scalar($data =~ s/(\w+)/\1/g) ];
dump [  length($data) ];

__DATA__
Line1 Word Something
Line2 Other Word
[download]

Gives:

c:\test>783947.pl
[6, 6, 6, 38]
[2]
[2]
[6]
[38]
[download]

Update: Another set of conflicting results I cannot immediately explain?

#! perl -sw
use 5.010;

$data = do { local $/ = undef; <DATA> };

say join ':',
        scalar( $data =~ tr[\n][\n] ),
        scalar($data =~ s/\n/\n/g),
        scalar($data =~ s/(\w+)/$1/g),
        length($data)
;

my $x = [
        scalar( $data =~ tr[\n][\n] ),
        scalar($data =~ s/\n/\n/g),
        scalar($data =~ s/(\w+)/$1/g),
        length($data)
];

say "@$x";


__DATA__
Line1 Word Something
Line2 Other Word
[download]

Gives:

c:\test>783947.pl
Use of uninitialized value in join or string at ...
6::6:38
6 6 6 38
[download]