So I've been playing simultaneous games of chess and shogi on this site, as I'm sure you've all noticed. My chess partner isn't very interested in trying shogi, and my shogi partner loves it far more than chess. I have to say that I love both games. Chess to me has such a beautiful balance that I am amazed. So many ranging pieces can be utilized together to create such amazing ballet-like combinations, it just astounds me. And though many don't realize it (since they don't play shogi), the finite number of pieces forces combinations and sacrifices to be done with care.
On the other hand, I really love shogi. Instead of great symmetry, it is extremely forward-directed. The pieces are substantially weaker, making for a slower opening game. But once armies begin to clash, it gets so exciting and difficult to anticipate. Players make sacrifices with less concern, because sometimess those exchanges, though for a weaker piece, gain a useful move not available to a stronger piece (a gold general for a knight, for instance). The difficulty of anticipating a player's possible drops makes the game so exciting, and yet a single mistake can turn the game around drastically.
Bottom line: players may advocate for one game or the other, but I can't help but love both games tremendously.