They're not going to be compatible. Look at the code on the PCM, and then look it up on an interchange site; you'll find that Jeep and Dodge 6.1 engines never come up in the same list.
Also, to make the PCM work in another car - even one where the PCM is a direct replacement - it needs to be programmed to the cars VIN and Mileage, and the keys need to be programmed to the PCM. That's not something most people can do at home, and it's not something that the dealer will do cheaply. In short - it's a last resort.
I would take Paulster2's advice, and look closer at the misfire codes. You mentioned that 'afaik compression, spark plugs and injectors were checked' - so you're not sure, therefore you should assume that nothing has been done correctly. Check the obvious first - swap ignition coils around (1 to 2, 4 to 5), and see if the codes change to show P0302 and P0305; if they do, then replace the ignition coils with good ones (don't get the cheapest; try to get OEM if possible).