There doesn't seem to be any research on these small canisters of oxygen, which are relatively new and have not caught on yet. However, supplemental oxygen is a recommended therapy for moderate AMS and here's an indicator of how much might be effective. This is from the Institute for Altitude Medicine at Telluride:
"Treatment of Acute Mountain Sickness
Supplemental oxygen 2 liters per minute in medical setting until symptoms improved. AMS headache typically resolves within 10-15 minutes of supplemental oxygen."
One small canister contains 9 minutes at 2 liters per minute, which is right at the minimum amount that typically resolves an AMS headache. If you're getting this same amount spread out over the course of the hike, it stands to reason that it would be significant at preventing the headache in the first place, which is what I find. I don't feel a need for constant use. With one of these in my pocket I can keep catching my breath very deeply every 5-10 minutes. Works for me and that's all I care.
I still plan to try Diamox on my next overnight trip to Shasta in June. I do not sleep well above 10,000 and the canister doesn't work as well because I have to wake up to use it and then fall back asleep. Diamox looks to be very beneficial for improving sleep at elevation, but from what I've read from Ken and others, the typical recommended dosages seem to be too high. With both of these working for me, I'm looking forward to a good night's rest and plenty of air all day. Clearly there is no magic bullet, so why not use all the tools available to make it a great experience.