My wife and I owned a Ford Crown Vic for ten years. It was a good auto which she drove in-town most of the time. When I occasionally drove it on the highway, a humming noise would begin at about 45/50 mph, and last until road-wind noise would mask it at about 70 mph.
The mystifying thing to me, and apparently to the Ford mechanics to which I reported the aggravating noise over the years, was that it was related to the accelerator pedal. When I took my foot off the pedal, it would stop, and when I barely stepped on it, it would start humming again. It was not a speed change that did it, but merely stepping back on the pedal.
A year ago, we finally traded it in for an '04 Jaguar S-type with 17,000 miles. I made the mistake of not driving it before buying, and it has the Ford Crown Vic accelerator pedal problem all over again. The Jag mechanic told me it was the differential, and there was no guarantee that if I forced them to replace it the noise would go away. In the proverbial Big Picture, this is a pretty small matter, but I would gladly pay for your response/comment/advice if it could bring an end, or at least a compromise, to my complaining.
The noise shouldn't be too much of mystery. Going by your description, it's a typical gear whine from the ring and pinion gears in the rear axle. Every set of gears produces a certain level of high-pitch sound while in motion, more prevalent at highway speeds while accelerating.
The whine often dissipates or disappears when you take your foot off the gas, because you're now applying torque to the opposite side of the ring and pinion gears' teeth. The big question is how much is too much. The sound will vary with the difference in engineering between one rear axle and another, correct adjustments such as pinion gear depth and backlash clearance, and the overall construction of the vehicle.
Luxury cars utilize more sound-deadening materials for a quiet ride, which can have a big effect on the level of gear whine transmitted into the passenger compartment. As in similar situations, while you're at the service department, ask to go for a ride in another S-type. If the same car produces the same amount of gear noise, then no, it wouldn't be worth the cost and effort of replacing the entire differential assembly. The noise may be an engineering characteristic common to this particular chassis and drivetrain.
If yours is significantly noisier than the other, then yes, it should be a condition that warrants repair. There are no current Jaguar technical service bulletins in publication regarding the complaint.