I really hate to step in, but I think it was cited xlp hi is something like 15 percent greater lumen ouput at same current level of 1 to 2 watts (v3 v s4, perhaps? I haven't studied the numbers fully, clouded by xpg rated at my preferred 350 to 700 ma, while xpl is 1500 or 1000ma. I suppose there is a cree calculator, somewhere out there. ) . So, why compare at same lumen when in real world you might get higher lux due to more overall output in a milliamp that most people would prefer due to battery limits and a reasonable runtime? Apples to apples, is ma to ma, more than lumen to lumen.
I would think same beam shape would certainly mean same lux if the lumens be equal, since lux is the net concentration of those lumens over any area. You can download an andriod trig calculator from eve-star to measure your hot spot and corona. So, it should be very possible to nail down beam angle of both in a standard p60. Also, measure lux of each at same drive level… . However, for lumen comparison- well, for last 3 years (as alternative to bulky sphere and ceiling bounce)- I also built an index card sized diffuser, made of three plastic frosted diffusers (I bought a broken overhead diffuser lens for $2 from home depot, not being wholly confident in the milk jug diffuser material) sandwiching in two white sheets of paper (glued together) , I store it in my lux meter case. Cheap, easy to store, easy to make, easy to use. Measure relative diffused lux at 2 feet(with nothing around, pressing diffuser to lens) and it does remarkable to compare over all output of lights with similar beamshapes. The diffused lux ratio gives you a multiplier. I don't bother comparing lights with radically differing beamshapes, or color, despite being a near perfect diffuser and nearly perfectly white. Key word is near.