If you have running issues on petrol but not on gas I would check that the MAF (Mass Airflow Sensor) is clean and bright. Because it is a hot wire in the airstream over time the wire can get all sooted up, reducing its sensitivity and this drives the fuel trims awry.
I had this issue recently with my 4.0 SE; it ran like a pig on petrol when it was cold but beautifully smooth on LPG. The first thing I checked was the MAF; it is the original dated 1997 and the interior of the sensor snoot was black as coal. I cleaned it and put it back on, connected it up and started the car from cold. The idle was transformed to rock steady without a missed beat, while acceleration is now crisp and willing.
It's very easy to do; unclip the sensor from the air cleaner and removed the hoseclip on the inlet trunking, unclip the connector by pressing on the wire underneath the connector and pull it off. Carry the MAF to the bench and spray brake cleaner or electrical switch cleaner into the snoot. You will see the silver wire emerge from the soot. Do NOT USE ANY OBJECT ON THE SENSOR WIRE because it you break it the MAF is fooked. Reinstal into the air trunking, reconnect and start her up. The older and blacker the MAF the better your car will run after its been cleaned - you won't believe the difference it makes!
If the cold-running problem persists then check the ECT (engine coolant temperature sensor) and the IAT (inlet air temperature sensor) because either can also affect cold fuelling.