With this NP-BX1 battery test fixture in hand:
The discharge tests run at 250 mA, which is probably a bit low, as the HDR-AS30V camera can capture video for about two hours on a single battery. Given the Sony’s nominal 1.24 A·h (love that precision!) capacity and derating the Wasabi’s ambitious 1.6 A·h, two hours suggests a current around 500 mA would be more appropriate, but we’ll go with a lower current for now.
Oddly, the two Wasabi batteries (green & blue traces) outperform the Sony OEM battery (red and purple) in terms of voltage:
I can’t explain the small kink just before the big dropoff for both Wasabi batteries. Perhaps the protection circuitry behind the battery terminals has a slight peculiarity?
Looking at the total energy delivered, however:
The Sony battery says it’ll deliver 4.5 W·h and actually produces 4.8 W·h. The Wasabi batteries claim 5.7 W·h and don’t even come close at 4.25 W·h.
I cross-checked those results by importing the CSV data into a spreadsheet, computing the point-by-point power, finding the average, and then multiplying by the total test time in hours. Doing it a couple different ways says you can eyeball a reasonable value by multiplying the median voltage by the test current to get average wattage, then multiplying by the total test time to get W·h. That’s within a few percent, which is good enough for me.
The camera’s power supply undoubtedly has a low-voltage cutoff, but it’s a single-cell battery and they might just run it down around 2.8 V; in that case, the Sony batteries will last longer. If the voltage cutout is 3.5 V, similar to the Canon camera, then the Wasabi batteries win.
I don’t have enough experience with the camera or the batteries to predict anything based on actual use.
The Smell of Molten Projects in the Morning 
For no good reason this reminds me of the time I had to calculate the stored energy in a pair of two-liter 4500psi carbon fibre air tanks. And then convince NASA that they should let me put the literally the energy of a stick of dynamite onboard their shiny new airplane… not to mention the enormous (4AH @ 24VDC if I recall) handmade lithium batteries right next to it…
Did they make you do the Rickover thing: sit next to your hardware during the first flight? [grin]