When to use multiple batteries vs a UBEC
A single battery powering everything is more convenient and reliable (only one battery to be charged and monitored etc.). It is generally better to use a higher voltage stepped down rather than a lower voltage stepped up. The battery current will be lower and voltage headroom can be higher, so there is less chance of a brownout during current surges.   

A 6V UBEC should operate down to 7-8V input voltage, while a good 11.1V Lipo will hold its voltage above 9V (3V per cell) provided its rating is not exceeded.   

Use a separate 6V 3A UBEC for each drive controller, another one for the servos, and a 5V 3A UBEC for the Pi and Arduino. With separate regulators you should not have any problem with interaction between power supplies.