So are LED bulbs brighter than CFL bulbs? In a recessed fixture, YES. Since ALL the light from an LED bulb is used in these, while a CFL bulb loses about half the amount of light it actually puts out (LED's have higher fixture efficacy). In something like a floor lamp where you need the light spread to be much larger (all around the bulb) then CFL's, at the moment are still more "efficient". 100% of the light they put out is used. (CFL's have higher fixture efficacy)

So what's the best way to measure brightness?

There's currently no standardized way of measuring LED bulbs that are used to replace traditional bulbs. The US Department of Energy and 3rd party organizations like Energy Star are trying to come up with ways to do so - but things like these take time.

As a result, many people are stuck with manufacturer's overstated claims and are many times burned (no pun intended) when buying LED bulbs by not getting the amount of light they were expecting. Also a lot of people are just looking at the total lumens that a bulb outputs. This was great when we were only comparing incandescent and CFL's, but with LED's as explained, the LED's use mostly ALL their light in a recessed fixture, while a CFL wastes a lot of light.

Until standards are finalized, if you want to buy an LED bulb and want to get what you pay for, rather than just guessing do the following:
Ask for side by side pictures of the bulb that is being replaced as well as getting footcandle measurements (with a light meter) for both (if possible). This will show and tell you that the LED bulb is giving the brightness and color that you're expecting as well as the beam spread (the 3 most important factors of an LED bulb).