It took a long time for them to call each other by their first name.
Call me stingy, but I get a little uncomfortable whenever someone in a fic calls Kaiba by his first name, Seto, just on a whim and that someone’s name isn’t Mokuba Kaiba. I think I heard that in Japan, calling someone by their first name is a sign of deep closeness and intimacy, and, Ryou and Kaiba aren’t exactly the most… intimate of people. They prefer their distances and personal spaces. So, until they get very, VERY close, they will continue calling each other by last name.
As for who says the first name first… My money is on Ryou, on a dare from Mokuba. Just to see Kaiba’s reaction. And then Kaiba will say Ryou’s on occasion, but I think he will use the last name more often.