Unfortunately PAR watts doesn't measure the energy that the bulb puts off which the plants use for photosynthesis and growth. It measures the energy that the bulb actually puts off as visible light, actually any light 400nm-700nm.
Plants use different wavelengths of light with different efficiencies. Red light is used with 2-5 times the efficiency of green light, but all wavelengths are treated equally when measuring PAR watts. This can be considered an improvement on lumens which count/----/--22 green light more than red light.
Also, plants use photons, not watts. Plant scientists use a PAR measure that actually counts photons. This is important because it takes 700W to make the same number of blue photons as you get from 400W with red photons but one blue photon makes the same contribution to creating sugar as one red photon (ignoring the other stuff that blue photons do like making leaves follow the light). So a 400 PAR watts bulb may be putting out exactly the same number of photons as a 700 PAR watt bulb. The makers of metal halide lamps love this measure because it makes their lamps look better relative to HPS bulbs. The metal halide bulb converts about as much energy into light as an HPS bulb, but creates fewer photons because they are bluer and each photon takes more energy.
So PAR watts are just another flawed measure, maybe a little less flawed than lumens, but also less useful because it is only published for a few lamps and the published numbers are difficult to verify.