I made one guess - count of possible wins of the first and
second player on the 4x4 board is in direct proportion to
count of their wins on the 4x2 board (due to the symmetry of
the 4x4 board and possible moves).

I have not managed to prove it mathematically,
so my program below may be totally wrong... :-)

###############################################################

#!/usr/bin/ruby -w

NEW_GAME = 0b0000_0000
END_GAME = 0b1111_1111

POSSIBLE_MOVES = [ 1, 2, 3, 4, 6, 7, 8, 12, 14, 15, 16,
                    17, 32, 34, 48, 64, 68, 96, 112, 128,
                    136, 192, 224, 240 ]
				
# wins_of_first and wins_of_second
$f = $s = 0

# last_move_by - true  for second player
#                false for first  player

def play( state, last_move_by, possible_moves )
     possible_moves.delete_if { |m| state & m != 0 }
     if state != END_GAME
         possible_moves.each do |m|
             play( state | m, ! last_move_by,  possible_moves.clone )
         end
     elsif last_move_by      # last move was by second player
         $f += 1
     else
         $s += 1
     end
end

play( NEW_GAME, true, POSSIBLE_MOVES )

puts "Wins of first  == #{$f}\nWins of second == #{$s}",
      "#{$f < $s ? 'First' : 'Second'} player is bounded to win"