Some of the device hardware/feature differences can be found at https://en.wikipedia.org/wiki/Roku
Similar spec comparisons can be found at Roku developer page https://developer.roku.com/docs/specs/hardware.md
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The 3820 does have a newer processor and more channel storage. An issue with how fast any of these devices are when released can change significantly when a new OS update is released by Roku. But generally, I would say you will probably a better experience using the 3820 over the 3810. It really depends on what kind of content you are streaming. (ie. channels/apps).
Here is a little image comparison compiled from the above wiki link of the 3810/3820.
click on image to enlarge.
