If I have both a BatteryPlus35-II and a MiniBoostPRO, both products will have solar inputs. Which one will become the dominant solar input device?

The dominant solar source will be the solar that produces the most power.

Solar installed on the roof will usually be the dominant source most of the time due to the number of panels. Most manufacturers will fit 2 or more roof panels.

If you want to use the solar function of the MiniBoostPRO, ensure it is fitted to the battery via a BC300 shunt and not to the AUX input.

For more information about the BC300 shunt, refer to the below link:
https://teambmpro.com/products/bc300-commlink-external-shunt