For playing a deeper, more complex game, opt for The Castles of Burgundy. For the shorter, simpler game, go with Kingdomino. The two games seem similar but feel dramatically different. Both games perfectly balance the competition for tiles with the personal satisfaction of building your personal province without direct interference. In both games, players take tiles from a central space and add the tiles to their personal princedom or kingdom board (depending on the game). For me, it's a toss-up between one of the best board games around in all categories, The Castles of Burgundy, and a solid game with killer two-player tile-laying action, Kingdomino. The person who hits the target more will win. Now hide behind the trees, target each other, and shot right on the target with cold water.
Many people have played Carcassonne, one of the most popular entries of the genre, but it's actually not the best example of the game - and certainly not the best for two players. Especially when you feel exhausted with heat, take your water guns out and fill them with cold water. Tile-placement games are a mainstay for many board game enthusiasts, in part because of the fun of building a unique board each time you play.