The old X308 XJR's aren't unreliable per say, but they are old now, and thus wear a tear will be a major cost factor in owing such a car. They drink fuel like a V12 more than a V8, average fuel consumption seems to be around 17mpg or so for them, less if you have a heavy right foot. They also chew through rear tyres fairly quickly, no surprise given they are heavy and have 400bhp and 400lbs/ft of torque. They do tend to have less expensive failure points than X350s with regards to the ancillaries, no air suspension for one thing and a far less complex electrical system. But they are by no means cheap to run.
I notice you said you wanted a nice big comfy car that's nippy, well to be honest an XJR is rather a few steps further than nippy, a MK5 Golf GTI is 'nippy' ...even quick, an XJR is very, very quick in a straight line. It's got 400bhp remember, or 390bhp if you get the slightly older version. It's seriously quick and that sort of power does not come cheap, having said that there are many cars that cost more to run and don't have the Jags brute force power.
The most reliable and cost effective way to get into big Jags now would probably be an X308 3.2 V8 ...still quick enough for most and very smooth with a lovely V8 sound. But, you will see more like 22-23mpg average, the tyres will be cheaper as it will likely have smaller wheels (not necessarily though) brakes are cheaper, and it wont chew through it's rear tyres as fast either in all likelihood, insurance is also cheaper. All in all cheaper to run, all be it still not at all 'cheap' though. Finding a good XJR from that era can be an issue now too, there are quite a lot of 3.2 V8s around though, the 4.2 N/A V8s are where I would put my money but they are hard to find as well, still if you can they have about the same running costs as the 3.2.
The XJR is a slightly different beast to the normal V8s though, has a lot of XJR only parts on it and quite frankly is more likely to have had the nuts driven off it at some point.
I think they are fantastic cars, I like the X308 better than the X350 is many ways (not all ways though) but they are old Jags and you have to realise what that could mean. Don't expect them to tick like a Mazda and stay cheap and cheerful forever. Chances are you will find most of the ones available for sale now have all sorts of stuff that's worn out or near to it and needs sorting to make the car drive like it is supposed to.
If you fully understand what you could be letting yourself in for though, there are far worse cars of this type to buy into, frankly they cost less to run than old V8 BMW's typically do and certainly less than similar Mercedes and less than Lexus too working on the assumption that you will have to replace parts on any of these. The Lexus might be the least likely to throw curve balls but even an LS400 is still an old luxury car, and bits wear out on those too and they typically cost more than Jag parts. Also, it's ruddy ugly compared to the lovely Jag