Best solution for FO's facing a steep authority gradient is to just tell the PIC he is welcome to be PF on both sectors it will save a lot of hassle for you and besides there are tons more flights ahead of you when you will get a more compassionate PIC who appreciates that there is more than one way to fly an aircraft.
From what I hear most of the arguments are about descent and approach at FZ.
There are many different ways and styles to fly a 737 so long as they are safe and within limitations the other flight crew should respect this and not try and intervene with his/her style of flying.
There are more and more ASR's with crew arguments lately only about 30% are being reported and documented.
This type of problem is becoming more and more serious at FZ.