Well they aren't cheap to run, but as V8's go, I wouldn't say they are particularly expensive, especially compared to the Germans.
The S-Type V8's will be cheaper to maintain than an X350 XJ because they do not have the complex and fearsomely expensive air suspension, when/if these go wrong, they can be eye wateringly expensive to put right, the S-Type doesn't really have anything like this. Although the older ones did have some gear box issues iirc, I imagine most of the mint high miler bargains would have had anything like that sorted already though.
The 4.2/3.6 Jaguar V8's are pretty bomb proof to be honest, it's the other bits that can cost the money on Jags. The older 4.0 nikasil lined V8 and I think also the 3.2 had some issues, but most of those are in the past now, and anything running around with one of these engines should be ok now, it probably either escaped the period of problems without issue or has been modified and fixed and will be fine. It was to do with high sulphur content of petrol in the late '90s and the effect on the nikasil lining of the cylinders in these engines, anyway you can read up on that issue in detail if you like, its well documented enough. Basically if it's a post 2000 car it should be fine, if it's an S-Type or an XK with a 4.2 V8 or is an X350 XJ of any kind, it's not affected anyway.