Connecting breakout board to Arduino with UART
Both the DigiX and the SIM908 are natively 3.3V boards. They should be able to connect to each other directly.

For some reason, the SIM908 breakout seems to only offer RS232 level serial outputs for the GPRS and GPS. On U3 (the SIM908 module itself) Pins 68/71 offer 3.3V levels for the GPRS (GPRS-TXD and GPRS-RXD) and 15/16 offer 3.3V levels for the GPS (GPS-TXD and GPS-RXD).

These are converted to RS232 levels by the MAX3232 and presented on J3 and J13. I can't see any point where the 3.3V signals are presented on a connector.

You could either:


Breakout the 3.3V signals onto connectors by modifying the SIM908
breakout board. 
Build a level converter to take the 3.3V signals from
the DigiX to RS232 and then connect them as before.


You may have damaged the DigiX board connecting RS232 levels directly to it however. The ARM based Arduinos are far less tolerant of voltage abuse than the ATmega based Arduinos.