For starters, the Trek 1 has a lensed bezel, which brightens & narrows the beam somewhat.
So making a direct beam-to-beam comparision is like comparing an orange with a genetically altered orange. They're close, but no cigarette. The Trek would win every time.
With the P3 on high or overdrive, both flashlights overpower their LEDs, and both are comparable when reflected output is observed - but as everyone knows, the tiny batteries in the Photon tend to sag pretty quickly when compared to those "AA" cells in the Trek.