What happens if both players get to 7 points at the same time?
The runner chooses who wins (and presumably chooses themselves) with the order they access they access the cards.  From the Rules Reference:


  When the Runner accesses cards in Archives, the Runner turns
  all cards faceup in Archives, then accesses and resolves each
  card in Archives one by one in the order of their choosing.


Also, as @LScottJohnson Points out in the comments:


  "If the Runner scores an agenda that gives him seven or more points, he immediately wins the game, even if he would otherwise access more cards."