Learn Italian: Casa tua è più grande di casa mia.

While possessives usually need an article in Italian, casa is a special case. When you mean "home" or "someone's place" as a personal concept, you drop the article and place the possessive after the noun. If you said la tua casa, it would sound specifically like your physical house or building rather than just your place.

Why do we use di to mean "than" here instead of che?

You use di when comparing two nouns or pronouns based on a single characteristic. Here, we are comparing two nouns (casa tua and casa mia) in terms of being grande. You would use che if you were comparing two adjectives for the same noun (for example, if a house is more big than beautiful) or comparing two verbs or prepositions.

Could I avoid repeating the word casa at the end of the sentence?

Yes, you could just say Casa tua è più grande della mia. However, notice that once you drop the second word casa, the possessive pronoun mia requires its definite article (la) again. The preposition di then combines with la to form della.

Could I use the irregular comparative maggiore instead of più grande?