Which transition mode for the four switch buck boost converter is correct?
you don't mention it, but this vonverter is bi-directional, energy (and net current) can flow either way, this is a good feature as it allows regenrative braking to recharge the accumulator.
Neither switching scheme  is ideal.
the second implementation doe not conduct current directly from input to output
this means that all current flows through all four MOSFETS and that the inducto does more work, as ai must convert all the power
the first implementation is more efficient when bucking (left side voltage higher than right) as the inductor is called upon to store less energy, - the inductor is only transferring the voltage difference when bucking
but when boosting with a fixed duty-cycle on the right side, it degenerates towards the first implementation when it's boosting.
Ideally you would drive whichever side wants the higher voltage with PWM and have the top mosfet on the other side on all the time.
in effect making a buck converter with an ideal diode or a boost converter with an ideal diode according to how you want to voltage ratio to be.