Just played my first two rounds as Battle Brothers, one against Havok Brothers and one against Ratmen Clans. In the round against the havok team, my unit of flamethrower-wielding Assault Brothers was decisive, so I suggested to the Ratmen Clans player he buy a lot of flamethrowers. He proceeded to buy 3 units of Rat Ogres w/ flamethrowers and 1 Rat Hero with a flamethrower and barbecue my entire team. I don't want to sound salty, but I'm starting to wonder how the A6 (6!!!!) Flamethrower is even remotely balanced. The close range seems to be the only limitation, and it is not too inconvenient.
I was crunching some math between AP and number of shots yesterday (regarding failed armor saves) and found depending on the target's base defense and the AP, 1 shot with AP went between 1.3 to 5 shots with no AP. however, IIRC, to get better 3 to 1 it had to be AP4 against a save of 2+, and most situations were in the sub 3 to 1 range.
Based on this, in almost all cases, if all else is the same, number of shots is better then AP. The flame thrower is the top of shots over everything else - IE if it costs the same any weapon at 2+ shots is better then a single shot weapon with AP (outside of AP4 and a really good save). Range is the only other balancing factor, however long range weapons tend to cost a fair amount for that range, meaning you have to be constantly moving to keep the enemy out of their weapon range and in yours.
I would have to see the full build lists/point totals to give you any armchair theory on what could have been done different. One thing that could be done is focusing on staying out of threat range (which would be 18" for the rat ogres w/ flame throwers, however that seems challenging. I will say that the flamethrower upgrade for the rat ogres seems cheep given that they start with no ranged weapons, but those melee attacks are rather scary. That said, 18" isn't simple to stay out of range of if your trying to also sit on points.