I've got a 2001 XJR and it's been great. I'm probably inviting some kind of electromechanical disaster upon myself by saying this, but mine's been remarkably trouble free, aside from the MAF sensor failing and the one of the window switches on a back door failing. I'm currently at about 80,000 miles so I'm starting to think about replacing the timing chain tensioners like 93EXCivic mentioned. If you go with an X350 they've got metal tensioners so you don't have to worry about that. The suspension is also getting worn out so I've started gathering parts to tackle that too.
If you're looking at replacing a minivan with an XJ, make sure you take a long hard look at the size of the trunk. Bring a bunch of stuff with you and try to fit it in - the full size spare eats up a lot of space and the gas tank sits between the trunk and the rear seat so the trunk isn't very deep. I use my back seat to haul stuff a lot more then I use the trunk because the trunk just isn't tall enough. On the plus side, I bought a 26 gallon air compressor at Home Depot and I was able to squeeze it into the back seat when it wouldn't fit in the trunk. The X350s do have a larger trunk than the earlier cars, but I'm not sure how much larger it is. Since it's an all new platform I'd imagine that they addressed that issue.
One last thing, when I was shopping for mine I found that the insurance prices for the all aluminum X350s was double the earlier steel bodied cars. I was told it was because repairing the aluminum chassis and body parts was much harder than steel parts. I don't know if repair techniques have improved enough over the last 8 years to bring the cost of repair down enough to cut insurance rates, or if it was so much higher for some other reason.
If you have any specific questions, let me know.
Just thought of something else - an open diff on a car with 400lb-ft of torque sucks. I can't believe Jaguar cheaped out on that. I don't know if the X350s have a limited slip diff or not, but I don't think they do.
Bob