Airbnb always charge the same as booking.com (about 20%), but some hosts can elect to pay 12% and the guest pay 8% (which Airbnb then break out as a separate fee).
Hosts can also elect to have no cleaning fee, but most can't. A hotel is always going to have better economies on shorter stays because they have in-house cleaning.
That's why you get lots of broken-down fees when you book on Airbnb, and why short stays are more expensive than with a hotel. Just look at the final figure and see if you think it's worth it.
Once you've confirmed a booking with Airbnb, you don't have to pay any more fees, or do "chores". If you're unlucky and book with a mad host who tries it on, their customer services will have your corner.
booking.com have the same arrangements with hosts as Airbnb, and the same 20% commission (the host pays it). There's no particular advantage to booking through them. I'd say Airbnb are better at rebooking you when something goes wrong on the day, but it's still a lottery.
If you can find a direct booking site, go for it and you should save! But Airbnb won't help if you send your money to a scammer, or the host rips you off somehow. I saved €1500 on a villa last year paying cash on arrival to a Spanish host - but that's not going to be for everyone.
100% of my direct bookings are from repeat guests, so if you had a nice time at an Airbnb, send the host a text and ask if they'll give you a discount for next time.