As other answers have pointed out already, the goal of splitting up the children was to reduce the chances of their discovery.
This also played a key role in the future, because Darth Vader eventually discovered he had a son, which led him to interrogate Commodex Tahn, the doctor who prepared Padmé's body for burial. Tahn took the secret of the second child to his grave, and until episode 6 only Yoda, Obi Wan, and Bail knew Luke and Leia were siblings. Vader didn't find out about Leia until he read Luke's emotions through the force, and Luke himself didn't know until after confronting Obi Wan's ghost.