How can I find out if my device uses FBE or FDE? Assuming that I have full access (root if neccesary) to a device running vanilla Android 8.1, how can I know if it is using Full Disk Encryption or File Based Encryption?
There are three ways to identify which encryption type is used:

Identification by device behavior

As a user you should be able to identify what encryption scheme is used by the behavior of your device when it boots (e.g. because you restarted it). 

If the classic Full Disk Encryption is active your device will boot for some time and then present a special password enter dialog. If you enter the correct password and confirm it the device will continue to boot which will take some seconds. Then after some time Android will be started and ask again for your password or PIN using the common dialog you should already know when you unlock your device.

If you don't get such a password request in the middle of the boot process you have most likely File Based Encryption (or no encryption at all). 

Read property via Termux

The terminal app Termux provides a command-line you can use for identifying which encryption mode your device uses. 

Start Termux and enter the following command: getprop ro.crypto.type

If the output is file your device uses File Based Encryption and block if it uses Full Disk Encryption. 

Read property via Android Debug Bridge (ADB)

If you have activated the development and ADB mode on your device you can connect it to your PC via USB and use the following command on your PC: 

adb shell getprop ro.crypto.type


If it returns file your device uses File Based Encryption and block if it uses Full Disk Encryption.