Yes, they would carry more energy than HPS lumen per lumen since HPS is of a higher wavelength than most LEDs, the lower the wavelength the more energy per lumen or per photon.
You are onto something here. The photon energy issue is a separate one from the lumen issue. 1 PAR W of HPS light is the same amount of energy as 1 PAR W of 3K LED, but the photon count is different and that is what drives photosynthesis. Red photons are less energetic and therefore require less energy to emit/create. On top of all that, we suspect that an even spread across the visible spectrum is ideal. So we want an even distribution as long as we are not sacrificing emitter efficiency to achieve it.