What's the difference between Ваша комната лучше нашей and Ваша комната лучше чем наша ? Are these interchangeable? If so, when should I use the construction «чем + nominative» instead of the genitive case?
Vernacular somewhat prefers чем — in line with how less inflecting, more analytical constructions tend to fare better colloquially. That doesn't mark the genitive construction as bookish, it sees everyday use too. However, the genitive often carries an added meaning of an implied "even" ("even better", etc.). In other words, you're likely to hear Ваша комната лучше, чем наша but Ваша комната лучше нашей — I'm using italics to show where the emphasis goes. Again, this isn't set in stone, it's just a tendency.