It definitely doubles the lumens, but you're right that there's something else going on - the eye perceives a doubling of light as adding about 10% more light. So it goes a little further, is a little brighter, but doesn't appear to your eye to be twice as bright.

Also, your eye adjusts to whatever the brightest light source around is. When you're in the country with no external lights, a 200 lumen light is sufficient. There's a section of bike path I used to bike just like this - trees, cover, no external light. My 200 lumen front light made things look like daylight where it was aimed. But the moment I got back onto streets with street lights, car lights, etc, my 200 lumen light looked underpowered.

And it's the same thing if your light has a hot spot - your eyes adjust to the brightest thing point of light in front of them.

That's why I like the shaped beam lights, like the Phillips Saferide or the Ixon IQ Premium. If the Specialized Flux turns out to actually have a shaped beam with cutoff, that might be the best - massive light output if you want it, less if you don't, often I don't because of the affect it has on vision outside of the main beam.

If it wasn't for the fact that it puts out so much light it's utterly blinding to anyone approaching it, the only thing I like better is the Seca 900 (narrower beam with more throw) on high combined with the Seca 1400 (wide, wide even beam) on medium. They have a semi-shaped beam, and it puts out so much light (with good color temperature and good color index values) it's obnoxious to ride with. Also, 2 lights, 2 batteries, and low battery runtime. But somehow it also does a good job of avoiding having a hotspot and also punching down the road.

In reality I ride with either the Saferide or the Ixon Iq Premium, because they're less hassle and do almost as good of a job - without being obnoxiously blinding. (I'm not at all saying all other lights are blinding, but the delibrately wide beam on that combination with high output is.)