If you and an opponent each control a Notion Thief, the replacement effects generated by their abilities will essentially cancel each other out. If the opponent would draw a card other than the first of his or her draw step, that draw will be skipped and you'll draw a card. The opponent's Notion Thief will then cause that draw to be skipped and the opponent will draw a card instead. Neither replacement effect can apply to this event again, so your opponent draws a card.