Looking at the specifications on the Roku developer site, the only difference shown is that the 3811 has a Amarillo 2019-HP code name, while the 3810 says Amarillo 2019. I have no idea what the difference is between the two, although I believe it is the WiFi radio. I think (can't say for certain, the developer's documentation doesn't go into that much detail) that the 3811 has what Roku refers to as a long-range wireless receiver. The power cord is the WiFi antenna, which substantially improves wireless functionality.
Every other spec that I can find is identical, so that's my best guess.
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