I responded to this question in your support ticket. So I am copy pasting my response here:
You are correct that technically both of them can be set in AP mode, so that a phone or computer can connect to them without a router. For RPi, this depends on how you set up the RPi linux system — you can set it in AP mode, but since that’s irrelevant to the firmware it’s just a matter of figuring out the correct commands to set the system in AP mode.
For OpenSprinkler 3.0, currently it only allows accessing firmware features when it’s in Client mode. The AP mode is merely used to configure the WiFi settings so it can log on to your router. There is no technical barrier to make it work in AP mode as well — it’s just that some of the firmware features, like obtaining weather data, perform NTP time sync, will not be available in AP mode, for the obvious reason that in AP mode it doesn’t have Internet connection. Other than that, it can fully function in AP mode.
That said, a WiFi router these days is very cheap, you can get a WiFi router for something like 10 bucks, then you can have your OpenSprinkler 3.0 and phone/computer connect to the router and communicate through the router. The router is not a modem, so does not need Internet connection. I suspect this is also more efficient for ESP8266 because in Client mode it doesn’t have to manage DHCP and other AP-related tasks.