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.
Dan Roku Stick (3600), Ultra (4640), Ultra (4670), Ultra (4800), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.