I am a native speaker from the middle of the United States.
Both words are understandable in your examples. In my opinion, I'd say that, "Sooner" is a more casual word. It would be more polite to use "Earlier".
Example, as spoken to a close friend:
He keeps getting there sooner than the rest of us. He gets the best parking spot.
Example, as spoken to a guard or to your supervisor:
He arrives earlier than us. He can, therefore, select the best parking spot.