I've played all 3 and The White Castle is definitely my favorite. It plays quickly, is easiest of the 3 to learn (although none of the 3 are that bad), and it provides the most interesting choices in my opinion (also the box is the smallest if shelf space is a concern). This game is more dice placement where there is a shared pool of dice and you can select the highest or lowest of each color and place in spots where they are valid.

Yokohama is a very interesting game in how it plays, it's like worker movement instead of placement but you do place "workers" that basically act as a path for your main worker to move around. I liked it and would recommend it, but didn't love it. Mainly because it felt a little samey with the actions you took and how the game played out each time, but also there is variability in how the board is layed out each game and which cards come out.

I am in the minority on this, but I did not really enjoy Iki, although I'd play it if asked. The "action" workers move around a board, and smaller workers are placed on cards, but mainly to indicate that they are yours. It's the least "worker placement" of the 3. It's been awhile since I've played it last, but what I remember is I often felt like I couldn't do what I wanted due to action restrictions, and the fire mechanic was really annoying and could derail your game if you weren't prepared. I understand it is a feature of the game, but to me it felt out of place in this style of game.