What happens when you fill your Pokédex is the same thing that happened in RBY, and indeed, the same thing that happens in RS. The guy in Celadon Mansion gives you a diploma. The one improvement in GSC is that if you have the Game Boy Printer, you can print off the diploma and actually get something solid out of it.
Similarly, when you finish the UnownDex, the odd machine in the scientists' building at the Ruins becomes usable, and it prints out images of the 26 Unown (there were sheets of blank stickers available for the Game Boy Printer, so you could make Unown stickers.)