In general, these two part numbers are the same device save for use in bus-powered devices. FUSB303B is an updated version of FUSB303, which can be optimized for bus-powered devices. A bus-powered device is a device that receives power from the VBUS connection of the USB connector, and usually does not contain a battery.
FUSB303 is designed to switch through the USB Type-C ErrorRecovery status every time the mode is changed or enabled. Depending on the design, capacitance, and power timing, the source time, the timing of this transition can sometimes cause the VBUS source to detect a detach. FUSB303B removed this transition through ErrorRecovery. Otherwise, they are the same equipment.