The GC didn't ship with a modem at all even in early not cost reduced models. There may have been some bundles with a modem for PSO1&2 or Homeland but there was only 4 games in its entire library that could even go online.
The Dreamcast had a built in modem and some models of PS2 had one built in.
The Dreamcast had a built in modem and some models of PS2 had one built in.