Yes, I have played Castles of Mad King Ludwig. Sadly, I have not played Between Two Cities but I have heard great things about the game, and love the fact that designers Matthew O'Malley and Ben Rosset along with Stonemaier Games and Bezier created a mash up of two very popular board games. Genius!
The game was great fun and quite dynamic, as you are constantly moving, and drafting tiles and building your Castles. The mechanic I especially loved, for those that haven't yet played Between Two Cities, is that you design and build not just 1, but 2 Castles, one with the player to your right and one with the player to your to your left, over 2 rounds.
Basically, on each round, every player is given 9 tiles to start. From those 9 tiles, you choose 2 tiles, and then pass the stack to the next player. You know that you will use 1 tile on each of your Castles (each tile helps you and your teammate acquire points and potential bonuses) though you don't have to decide until placing which tile will go where. Thus, you effectively have 3 teams you are on in Between Two Castles of Mad King Ludwig. You have a teammate to your right, and a teammate to your left, and you also have a team of just you, as there is a single winner of the game.
How does that work you say? Well, another ingenious device employed by the designers is how the scoring works. Players do not win by scoring the highest Castle. Duh! Were that to be the win condition, I could easily ditch one of my castles and focus all of my energy on the other. NO - the win condition is the player with the high score, however, the high score is the lower score of your 2 castles.
Thus, while you want both of your Castles to do well, you also want to consider how well your teammates' other Castles are doing, so that you can act accordingly. I say this sort of in speculation, as it was everyone's first time at the table playing; how you are supposed to simultaneously help your teammate and Castle out while also peering over their shoulder to see how well their other Castle is doing, while keeping them motivated, I don't know! I guess I will have to play again!
In any event, I loved the fact that it was both cooperative and competitive, and that each player had 2 teams to play on. Furthermore, the end game scoring is an experience of itself. We did it Castle by Castle so the suspense was quite a trip, as you can't know who has won until every single Castle has been tallied, and so is sort of a game in of itself.
For the full rules, see this pdf.