Most if not all these 6v 12v boost drivers are using a High-Efficiency, Fully Integrated, Synchronous, Boost Converter MP3431.
After 100ma output the efficiency is almost identical with either 6v output or 12v output. The difference being around 3 to 7% less for 12v depending on input voltage. Both should be about 90% efficient with a voltage over 3v in with over 100ma output.
Its the same Boost converter used in this driver. [ GXB172 - 50W Single Cell 17mm Boost Driver! ]
I built a couple and changed a few resistor values that allow 12v operation at 3.2 amps usig a xhp35.2 led. The MP3431 is rated at 50 watts but I pushed it a little over 60 watts, its a beast.
Data sheet for MP3431. Efficiency data is about 1/3 down the page.
https://www.mouser.com/datasheet/2/277/MP3431_r1.0-1384411.pdf
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I’ll add that these drivers from china are probably not built with some of the best components like Loneoceans driver. They may handle more power mods fine and they may not.