Booking.com uses the Agency model, this means the website is a place where hotels list their offers and booking.com gets a commission with every booking done through their website.
On the other hand, Agoda uses the Merchant model in addition to the Agency model, meaning that in some cases they actually buy the hotel rooms from the hotels directly (in bulk), then offer them at a competitive price. I think they do that a lot with Asian Hotels.
That's why sometimes Agoda is cheaper, other than that it's just a psychological effect because they show prices per night and tax-exclusive, which gives the impression that their prices are less.
One more thing, Booking Holdings (the company that owns both Booking.com and Agoda) is doing a great job, they are doing a business trick where people think that both sites are major players which are competing with each other, so customers think they must choose between one of them, whatever customers choose the company earns money. This is called "self-competition" in the business world. It's also called "The Illusion of Choice" (thanks to @RyanfaeScotland for pointing that out).