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Gentlemen, let me stick an oar into these murky waters. My first question
is: what do you mean by 'big board'? If you accept FIDE as the standard,
then anything above 8x8 is 'big'. I would argue against that and the
ideas that you need really powerful pieces, or even many pieces, and more
than 1 move per turn. (At least up to, say 25x25 ;-) At 19x19, Go does
quite well with merely putting non-moving pieces on the board one at a
time. I've worked at 'large' sized boards (10x8, 10x10, 9x21, 16x16)
and, now that I'm looking at it, the general trend is the larger the
board, the fewer the pieces, and the ranges in 'linear' distance often
decrease, but that's because the 9x21 is conceptually also 3x3x3x7 and
the 16x16 is similarly also 4x4x4x4, so you can't go very far in any one
'direction'. Okay, you might think that last bit is all bs, but Go still
elegantly demonstrates you don't need powerful pieces for a large board.
And the 9x21 game (189 cells) is a chancellor chess variant using only the
standard 9 pieces and pawns per side of chancellor chess. The 16x16 game
(256) uses only the standard 8 pieces and pawns of FIDE per side. 
Andy Thomas has made some excellent points. I think he's right in all of
them. I just need to know what size we're talking about, and am curious
about the line between chess and wargames, like say 'Axis and Allies'. I
would recommend HG Wells book 'Little Wars' as an excellent example of
what is clearly over the line. (It's also got great photos.)