If you know after each team gets a possession that the OT will still be tied, then you would want the ball first on the next possession. Because next score wins.
This is akin to calling to receive in the old overtime rules where 1st team to score wins.
So there is logic to take the ball first.... but only if you've got some crystal ball or you really really believe that the game will go into OT.
However, playing Princess Bride here... if you know that I know that you know that if the 1st possessions end in a tie, then you will have an advantage because you get the ball first on your second possession, Then in my 1st possession of OT, I will be very aggressive and try to end the game then.
If:
1) you have confidence in your offense and/or
2) you know you have a shaky kicker and/or
3) you don't have confidence in your defense holding,
Then the latter would probably play out more. But we don't really know since this hasn't happened before.
