Questions & Answers about Mój dom jest większy niż twój.
Does niż change the case of the word that comes after it?
No, niż (than) just connects the two things being compared, so they match in grammatical case. Because mój dom is the subject and is in the basic nominative case, the thing it is compared to (twój) is also in the nominative case.
Can I use od instead of niż to make this comparison?
Yes, but the grammar changes! If you use od (which also means "than" in comparisons), the word after it must be in the genitive case: Mój dom jest większy od twojego. Using niż is often easier because it doesn't force a case change.
Why is the word for "bigger" większy when "big" is duży?
This is an irregular comparative form. Just like English changes "good" to "better" instead of "gooder", Polish changes duży to większy. It ends in -y here to match the masculine noun dom.
Why does the sentence use twój (your) for "yours"? Shouldn't there be a different word?
Polish doesn't have a separate set of pronouns for "yours", "mine", or "ours". The word twój means both "your" and "yours". You can safely drop the second dom because it's obvious from the context, leaving just twój at the end of the sentence.