If they don't behave the same, it's fair to assume something is different. Possibly several somethings. It helps to be systematic when fault-finding and to only change one thing at a time.
Personally, I'd swap the gas jets between the burners first (I'm assuming you are using MIG tips for gas jets) and see if the imbalance follows the jet.
If it makes no difference, try swapping the flares next (I'm assuming the flares are not fixed: you seemed to be adjusting their position in the video).
Do all your initial looking for the differences with the chokes fully open to take them out of the equation.
My feeling with burners is that, ideally, you want to get close to an all-primary-air flame (almost all hard central cone with minimal bushy outer flame) with the chokes fully open, giving the highest flame temperature. Then you can adjust the flame temperature down (and make the forge atmosphere more reducing) by closing the chokes.
It's important to understand that the choke adjustment varies the temperature of the flame, whilst the pressure adjustment varies how much of the flame there is.
For mid-range temperatures, you can usually get the forge temperature required either with a lot of relatively cool flame, or with a little relatively hot flame. Many people focus on gas consumption and try to run with the small, hot flame. Others focus more on the scale and decarb situation and tend to accept a higher gas consumption as the price they pay for a reducing forge atmosphere. These guys run a bigger, cooler flame.
For welding, you usually need quite a lot of very hot flame and do not really have as much choice over settings.
