First, if you ask politely and diplomatically by e-mail or phone, you might get the hotel to match the rate you are being quoted by Agoda. That might take a manager to get involved, not just whoever answers the phone or e-mail. Or, you might find that Agoda had access to the smallest or least desirable room, so a lower price.
Also, while this experience occurred in Spain a few years ago, I was by the front desk of a lovely small hotel, when the desk manager was dealing with a phone call about a reservations problem. When she finished, I asked her if she had a lot of problems or misunderstandings related to reservations. Her reply was that they dealt with many different booking services, and that they never had problems with Booking.com reservations, but had numerous problems with all the others. Interesting comment.
I have almost always booked through Booking.com, although sometimes directly with the lodging. Always been happy with Booking.com. Solid reviews by past guests, descriptions which generally include square footage, frequent traveler discount, and great customer service when needed.
PS: I must admit I have never heard of Agoda.