If they only have one more creature than you, both Oaths will trigger, however, only one will resolve successfully. This is due to the second oath trigger being countered because "target player who controls more creatures than he or she does and is his or her opponent" will be an invalid target after the first trigger (assuming you hit a creature). If however, your opponent controls 2 more creatures, you may elect to oath twice.
At the beginning of each player’s upkeep, that player chooses target player who controls more creatures than he or she does and is his or her opponent. The first player may reveal cards from the top of his or her library until he or she reveals a creature card. If he or she does, that player puts that card onto the battlefield and all other cards revealed this way into his or her graveyard.
