Lupin III: Cagliostro no Shiro

This has a lot of similiarties. Such as kidnapping, brave heroines, innocent princesses, love between boy and girl and a lot of different things. 

Both of these films involve a girl that the male protagonist takes an interest in. But the girl is being used by the villains, and the protagonist fights to try and win the girl and also fulfill his personal dreams. With that said, the major differences are that Laputa: Castle in the Sky is more innocent, since the main characters are younger. Lupin is a bit more fun to watch because of his antics, while Laputa strikes me as a bit more serious at times. 

Both have castles and revolve around stopping an evil count's schemes. While 'Castle in the Sky' is more innocent in nature, 'Castle of Cagliostro' is more lighthearted through comedy, even with the few darker undertones it has. Both were made by Hayao Miyazaki, with 'Castle of Cagliostro' being his first film.  

the animation style is very similar. Obviously the characters are very liekable, with Lupin being just as adventerous and quick-witted like Pazu in many situations that come up. There are also very exciting battle scenes (and explosions!) and in the end (spoiler), original monuments get destroyed to make way for the peace of natural beauty and prevent the greediness of the evil to prevail. 

Both share the same feeling : heroes are so cool, adventures are great, life is good. In both there is 2 male heroes, 2 good friends who share adventures : one is the coolest, the hero of ladies, the most adventurer ; the other one is the great partner, the loyal friend, always there. Both share the same spirit, heroes are outlaws, but the good guys, in one word : they are free ! So I think if you enjoyed one, you'll probably like the other one.  

Both anime feature a main protagonist who is seeking to solve an ancient puzzle. Also, both deal with kingdoms, castles, traps and shady villains. However, both are light-hearted anime and do not take themselves too seriously, opting instead to entertain the watchers.