Best avoid the 2x TC on any zoom. It is best suited to fast primes, and even then it greatly decrades IQ. The 1.4x works pretty well on zooms and can be very good on a decent prime.
I didn't think the Canon 1.4x worked on the 70-200 or is it the 70-300L I'm thinking of.
The 2x TC wil not AF with the 70-200 F/4 on any crop body.