[atleastoptimal]

Supply and demand. Fewer AirBnB's mean more will use hotels who will otherwise use AirBnB, leading to hotels increasing their prices, even though they compete with each other.

[hypeit]

There's no shortage of hotel inventory in NY. The supply is there. Hotel pricing didn't change at all in NY pre/during/post-Airbnb.

[RC_ITR]

And the supply of apartments for living in will go up by exactly the same amount.

Supply and demand works in both directions.

[atleastoptimal]

They're not the same markets so not comparable in that sense. Even if it equalizes eventually, price will increase temporarily.