hi, I have recently bought a gameboy and have an issue?

Well I recently bought a gameboy for one of my sons and then was going to buy another for the other son now He has bought several games and I was wondering if i bought another one for my other son and bought a link cable will they be able to play against each other and if yes then will I need to buy the same game for it e.g

One gameboy sp has sonic advance as a agem now he links the Cable to the other gameboy but will the other gameboy need to have a sonic advance cartridge as well?