A very good question. I'll explain what I know for each park:
Tokyo Disneyland - from what I've heard, TDL was designed almost by a shopping list. If you go to TDL, you'll notice that almost all the rides are clones of the "best" version of each ride at either Disneyland or Magic Kingdom. DL's Pirates, HM's Haunted Mansion, DL's riverboats, etc. This is because the Oriental Land Company executives (who were funding the park) took tours of both Disneyland and Magic Kingdom, and pointed out what they wanted from each park. WDI didn't complain much, as they were hard at work at EPCOT Center, which was supposed to open the same year, and it saved them a lot of resources on creating new attractions. It does, however, mean that Tokyo had very few original rides at opening, and had a copy of Cinderella Castle, which the executives apparently liked better. The two castles have been painted differently in recent years to distinguish the two, though.
Disneyland Paris - although the castle is themed to Sleeping Beauty, it is technically named differently (Le Château de la Belle au Bois Dormant), and is of course a radically different design. It's far taller, more elaborate and more "fantasy" than Disneyland's version. Supposedly, there were plans to theme the castle to the then-upcoming Beauty and the Beast, but Eisner was uncertain about having the the castle themed to a movie which may have failed at the box office. It therefore became themed to Sleeping Beauty at some point in the design process. Eisner should have known better... Walt themed Disneyland's castle to Sleeping Beauty, even though the movie didn't come out til 4 years later. Why they didn't theme the castle to Snow White or another movie of proven success is a mystery to me. One could argue that they chose it because Sleeping Beauty is a French folk tale, while Snow White was German and the Little Mermaid was Dutch (and the Imagineers weren't eager to clone Cinderella's Castle for a third time). At the end of the day, I wouldn't blame Eisner here... regardless of theme, DLP's castle looks by far to be the most beautiful castle in the world, matching the rest of Disneyland Paris.
Hong Kong Disneyland - 100% because of design costs. The park's small size demanded a smaller castle, but they didn't necessarily have to clone Disneyland's castle exactly. Park press releases claimed both the castle and Main Street (which was also mostly cloned from Disneyland's) were built in "tribute" to Anaheim's Disneyland, which opened 50 years earlier to the day, but that was mostly fluff. The HKDL project had its budget slashed so badly throughout its design that the Imagineers had little budget to devote to things like developing new castle proposals and plans, or even things like Fantasyland dark rides or, well, Frontierland. Say what you want in defense of Michael Eisner, but his regime is entirely to blame here. I'm sure there were plans at some point for a more unique castle, but I doubt we'll ever see them.
Rumor has it that Shanghai will have a completely unique castle... I hope those rumors are true.
Knowing franchise-heavy Bob Iger, I'm betting on Rapunzel, but I wouldn't object to a Beauty and the Beast or Snow White either.
