Should I use booking.com, airbnb or any site like that? Why should I? Are there any advantages?
The only major advantage is price: it's not uncommon for a third-party site to have better prices than those offered directly by the hotel. That said, major chains are increasingly offering best-price guarantees, although these usually only mean that you can claim the difference if you spot it, not that they're actually always the cheapest option.
Minor advantages include:
But all that said, I still book directly through the hotel if I can. Your reservation is less likely to get lost, you may get better rooms and more perks, making changes to your booking is easier, and you'll get points if you belong to the hotel chain's frequent traveller program.
Also, Airbnb is (supposed to be) for person-to-person short stay rentals, not regular hotels. For most of the properties listed there, Airbnb is the only option for booking.
I use both depending on the situation.
When I use an aggregator it is only booking.com and airbnb. Outside these two I book directly through the primary site.
Booking.com has three features I like very much.
I use airbnb for personal holidays with the family. Usually hotels and hostels are quite costly if you need accommodation for a family trip.