Datasheet

Both can use a 3.5mm headset

Both recharge over the microUSB jack

Both have a buzzer driver

Here's key differences

Size: the SIM808 based FONA breakout is larger. Shields are the same size

The 808 has a GPS module integrated as well

The 800 has external 8 ohm speaker driver (external audio) whereas the 808 has only headset audio and 32

ohm speaker driver

The 800 has an FM tuner for listening to radio