Difference between Roku 3930 and 3960?
You pretty much got it.
The 3960 is the newest Express HD model. It is dual band (2.4ghz and 5ghz) and has the ability to connect to the ethernet through a compatible USB-ethernet adapter. It also received a bump up in storage from 256mb to 512mb and should be faster than its predecessor the 3930.
You cam get an idea of their hardware and specs from this wikipedia entry. https://en.wikipedia.org/wiki/Roku
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Since the Roku devices are currently on sale, you may want to consider the Roku Express 4k+ (3941) for $25 over the Roku Express HD (3960) on sale for $18. The 3941 will come with better hardware and memory specs and also includes a Voice Remote with TV controls.
https://www.roku.com/products/players/compare
https://www.roku.com/products/players
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As for the extender part of your question, it is likely the newer devices will connect easier with the addition of the 5ghz band. With extenders, there are a few things you have to configure and take into account like dead zones, overlapping zones, etc. The 3930 should be able to connect to an extender, but may need to setup extender to recognize the 2.4ghz band and use a different SSID name to force connection. (or at least know when it is connected to extender).
Just because an extender is closest to the device doesn't mean it will connect to that access point without a bit of configuration. Much easier to configure a network with seperated bands (seperate 2,4ghz and 5ghz bands) and extenders than when using a mesh system with pods/extenders.
It can be a hit/miss situation with devices and extenders and may also necessitate moving some equipment around to achieve the desired result.
