Which is resolved first, new obstacles or new crossfire level in Shadowrun Crossfire?
I think that you've got your order of play mixed up a little bit. Let's review what the order of a round is:


  
  Draw a new Crossfire card.
  Each runner takes a turn, beginning with the starting
  runner. Play continues clockwise until everyone has taken a turn. The starting runner remains the same throughout the game.
  The round is over. Repeat steps 1–3 until the game ends. (Rulebook, pg. 12)
  


Missions go over the course of a number of Scenes. The Extraction mission has the following rules for ending a Scene:


  Mission Progress Track and Ending a Scene: At the end of the Client’s turn, advance the mission-progress marker to the next round down on the track and follow the instructions for that step (see Obstacles and Crossfire, above, for obstacle placement). (Rulebook, pg. 20)


So a scene ends, and obstacles are drawn, immediately at the end of a Client's turn, which will happen during Step 2 of a round, and then will be followed by Step 3 when any end of round effects are resolved. A Crossfire card is then drawn during Step 1 of a round. So there will never be a conflict between new obstacles and new Crossfire cards because they happen during different steps of a round.

Also, if you end a turn with no obstacles (and therefore remove a Crossfire card), the Shadowrun: Crossfire FAQ clarifies that you do not draw a new Crossfire card immediately, so again there will never be a conflict between a Crossfire event and obstacles.


  Q: I’ve just ended a turn with no obstacles in play, so I remove the current Crossfire card from play. Now I draw another one, right?
  
  A: No. You only draw a new Crossfire card at the start of a round of play. Depending on when you removed the current Crossfire card, it might still be several turns before you draw a new one.