It’s all to do with the radius of the curve, most pistol grips having a curve of relatively tight radius, while the ‘Prince of Wales’ follows a very much more open curve.
It all works like this: The classic English double-trigger side-by side shoots and handles best for most people with a traditional straight-hand stock.
That’s because the shooter is easily able to slide his trigger hand very slightly backwards, without materially altering his grip, when he pulls the back trigger.
With a single-trigger gun, which most modern over-unders are, this is not a necessary requirement.
The trigger hand stays in exactly the same place while both barrels are fired, so the grip can be at the most comfortable angle possible.
However, in the case of the double-trigger gun, some compromise is possible, and some shooters find the slightly curved Prince of Wales handgrip more comfortable than the straight-hand stock, and still allowing for a slight change of grip between trigger pulls.
The Prince of Wales (the one who became King Edward VII) had his guns stocked in this manner, hence the name. One contemporary report records that, on a double-gun day, he had four pheasants dead in the air at the same time.
That’s not only brilliant shooting, but indicative of first-rate teamwork by the Prince and his loader.