For almost any game, the counterpart to elegance will be flavor/variability.
Consider this: there isn't just Western chess, but a number of other widely-played chess-type games: the Chinese game xiangqi, Japanese shogi, and thousands of variants thereof, all descended from Shatranj. It's not too difficult to come up with a simple change to chess, like "What if each player started without knights and could drop them anywhere as a move?" (that's called "Pocket Knight Chess") or "What if, after every move, you had to advance an enemy pawn?" (that's called "Avalanche Chess"). Shogi and Xiangqi invite other possibilities to consider, such as giving pieces their own unique promotions (like the rook becoming a "dragon king" in shogi), or modifying the terrain (like the palace in xiangqi which the king can't escape).
In that particular respect, go is a bit more limited; there are only a few changes you could make which amateur or professional go players would be happy to try out during casual play. Meanwhile, two different grandmasters have invented their own versions, one by introducing new pieces (Capablanca Chess) and one by randomizing the opening (the better-known Fischer Random Chess). This could, of course, be seen as a sign that chess has "hit a wall" in contrast to the continuing explorations in go, but, hey, whatever. I actually prefer designing games, and even just reading their rules, to playing them. Because of this quirk, I would have to answer this not-terribly-important question with "chess".
Come to think of it, there's much more important criterion to consider — which game plays better on a rollercoaster
. In terms of how it looks, the answer is once again chess.