Bet you saw this one coming a mile away, right? Two miles away? Wow, those are some good reading eyes you're sporting there.
Yes, Prince Caspian is definitely a fantasy novel, in no small part thanks to Narnia. An other-worldly land that can only be accessed by magic items and that's filled with talking beasts and mythical creatures? It's a pretty fantastical setup and requires a good deal of suspension of disbelief on the reader's part.
Given that—and the lack of space ships, ray guns, and aliens from the depths of Nebulian XII—we're going with fantasy here.
Sure, Prince Caspian lacks Jack the Dog, but it makes up for things with Reepicheep the mouse and Trufflehunter the badger. But it's not an adventure because it has talking animals (though that doesn't make it not an adventure, either).
Instead, it's the risks, the exciting tasks, and the derring-do the characters undertake to reach their goal that put this novel squarely in the adventure category. Peter, Susan, Edmund, and Lucy are attacked by a vicious bear, must trek over a dangerous gorge, and are attacked by Telmarines. And that's before they even reach Prince Caspian and the war. After that, they prevent the resurrection of the White Witch, Peter fights a duel with a wicked king, and Lucy and Susan help Aslan free a rivergod.
Adventurous summer vacay? We'd say so.