It should not be at all surprising that different people choose different offers: the short-stay accommodation market (let's say 1-30 nights) is characterised by a great deal of product differentiation and yield management. Airbnb has reciprocity at play, as guests and hosts switch roles. Additionally, hotels and airbnb hosts have different cost structures and different business models.
Furthermore, consumers have different amounts of information: bounded rationality and satisficing are at work. So even if the offers were identical (they're not), and people's preferences were identical (they're not), then people would still make different decisions.
product differentation
Although you always prefer a lower-cost hotel-room to airbnb, some other people will prefer airbnb, even when presented with identical information. That's because they are not identical offers: they have many different characteristics (flexibility, physical space, presence of host, services offered, location, the P2P feelgood effect, doing business with individuals rather than faceless chains, staying in someone's unique home rather than just another clone room that looks almost identical in most of the world). And different people weight those characteristics differently: no two consumers have identical preferences.
yield management
Different people will also be booking at different times, with varying flexibility. Hotel rooms, (like airline seats), are one of the paragons of yield management, used in many textbooks' explanations of it.
reciprocity
Because with airbnb hosts can become guests, and guests can become hosts; and because reputation plays a major role in the market, there is reciprocity at play: both sides are incentivised to deal fairly with each other, rather than the practice of many hotels of making repeated attempts at getting more and more money from the customer from additional goods and services sold in addition to the basic accommodation, sometimes by using deception in the initial offer.
cost structures
On the supply side, airbnb and hotel rooms have different cost structures: an hotel room that's empty for the night is a wasted asset, and there may be little opportunity to reduce associated costs. Whereas a home without an airbnb guest is still a home, the residents get to have it all to themselves, and don't have to do any additional hosting, laundry, cleaning or tidying.
business models
A hotel's entire income is dependent on it renting its rooms out and selling associated services. For an airbnb host, the airbnb income is usually an additional source of income, a bonus rather than the thing that keeps a roof over the head and puts food on the table. So there is not an urgent and immediate need to find a guest, allowing them to set higher prices and tolerate a lower take-up.
