Which side is best to stay on in Budapest?

As a traveler exploring the vibrant city of Budapest, I'm curious about the best side to settle in. Should I venture to the historic Buda Castle district, with its stunning views and rich cultural heritage, or delve into the lively Pest side, known for its bustling nightlife and modern architecture? Both offer unique attractions, but I'm seeking guidance on which side offers a more well-rounded experience for a first-time visitor. Could you weigh in on the pros and cons of each, helping me make an informed decision?