I wasn't entirely sure which of the square brackets you wanted to capture. Just swap instances of

( \[ [^]]+ \] ) \s+
[download]

with

\[ ( [^]]+ ) \] \s+
[download]

(and vice versa) to suit.

#!/usr/bin/env perl

use 5.010;
use strict;
use warnings;

my $s1 = "REMOTE     [Mon Jul 16 21:49:33 2012] @@ [ueh1] [TNT] [20490
+] [1916]  0.0- 1.0 sec  0.33 MBytes  2.74 Mbits/sec  6.056 ms    0/  
+233 (0%)";
my $s2 = "REMOTE     [Mon Jul 16 21:49:34 2012] @@ [pdn1] [SSH] [20499
+] [3]  1.0- 2.0 sec  0.34 MBytes  2.86 Mbits/sec";

my @strings = ($s1, $s2);

my $re = qr{
    \A
    REMOTE \s+
    \[ ( [^]]+ ) \] \s+
    ( @@ ) \s+
    ( \[ [^]]+ \] ) \s+
    ( \[ [^]]+ \] ) \s+
    ( \[ [^]]+ \] ) \s+
    \[ ( [^]]+ ) \] \s+
    ( .+? ) \s+ sec \s+
    ( .+? ) \s+ MBytes \s+
    ( .+? ) \s+ Mbits/sec
    (?>
        \s+
        ( .+? ) \s+ ms \s+
        ( .* )
        |
    )
    \z
}x;

for (@strings) {
    say for ('-' x 60, $_, '-' x 60);
    m{$re};
    say for grep { defined } ($1, $2, $3, $4, $5, $6, $7, $8, $9, $10,
+ $11);
}
[download]

Output:

$ pm_str_remote_re.pl
------------------------------------------------------------
REMOTE     [Mon Jul 16 21:49:33 2012] @@ [ueh1] [TNT] [20490] [1916]  
+0.0- 1.0 sec  0.33 MBytes  2.74 Mbits/sec  6.056 ms    0/  233 (0%)
------------------------------------------------------------
Mon Jul 16 21:49:33 2012
@@
[ueh1]
[TNT]
[20490]
1916
0.0- 1.0
0.33
2.74
6.056
0/  233 (0%)
------------------------------------------------------------
REMOTE     [Mon Jul 16 21:49:34 2012] @@ [pdn1] [SSH] [20499] [3]  1.0
+- 2.0 sec  0.34 MBytes  2.86 Mbits/sec
------------------------------------------------------------
Mon Jul 16 21:49:34 2012
@@
[pdn1]
[SSH]
[20499]
3
1.0- 2.0
0.34
2.86
[download]