The new buildings are barely full. The 1BR rents are approximately $2,400/mo, depending on where it is located. A 2 BR in a new building across the street from the VA Hospital in Jamaica Plain rents for $2,750/mo. Market rate apartments in Boston are looking for customers. The owner-occupied rentals are better deals, usually, because you will get more for your money. More square footage and neighborhood feel. Owners were forced to register their apts rentals and AirBnB rentals by new policies enacted by the City of Boston. The other cities and towns have their own rules.
New York feeds 22% of the renters shopping for market-rate apartments, followed Chicago, Los Angeles, and Miami. Residents in New England states move in for jobs. For those who are leaving Boston, they move to more affordable towns and cities.