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In chess, the traditional 'odds' system has a couple of difficulties in
being made into a systematic method for handicapping.  In its original
context (usually, chess clubs where games were played for money) it made
sense, but in modern times, there is the problem that two beginners can
play at rook odds, and the weaker side will still occasionally win, but if
grandmasters played at rook odds, the weaker side could not possibly win. 
Ralph Betza has written on this extensively.

Also, there is the issue (which I think is the source of what I mentioned
above) that in an odds game, the side with more materiel may adopt the
strategy of attempting at every turn to simplify the game into a winning
endgame.  Of course, this is what chessplayers do ordinarily once they
have established an advantage in materiel, but in odds games, it adds a
late middlegame flavor to even the opening, and fundamentally changes the
game.

Shogi does not have this problem, because when odds are given in shogi,
the stronger player starts without one or more pieces (not in the other
player's hand; just eliminated utterly from the game), but if side with
materiel advantage attempts to capitalize on this by offering exchanges,
it actually complicates the game, because now both sides have pieces in
hand, and a piece in hand is more valuable to the better player than the
weaker one, so this strategy is counterproductive.