I have two floodlight fixtures on a single switched circuit. Each fixture has a pair of 150 watt bulbs for 300 watts per fixture or 600 watts on the circuit. I want to replace one of the fixtures with a fixture that has a motion detector as is commonly sold in hardware stores. Like the fixture it is replacing, the new fixture has two bulb sockets. The specs for this new fixture say "Lamp holder wattage up to 150 watts each, Total lighting wattage up to 300 watts".

My question: Does the 300 watt maximum apply only to the combined wattage of the two sockets on the new fixture or do I have to include the wattage of the bulbs on the other fixture on the same switched circuit?

The specs 150W per socket is what it says, one socket cannot have more than 150W - probably due to heat considerations. It doesn't say anything about the motion detector however.
If the motion detector is an inherent part of the fixture, then it probably is designed for only 300W too, but you may have got different specs for it if it is a separate assembly. Or maybe something is written on a label attached to it.
If nothing indicates that you may connect more than 300W to it, then don't do it.