Don't have direct comparison between WR A4 and D4 on the same car, I've got the A4 as 205 55 16 (94V XL) on my GTD, my mom has the D4 on her Toyota Corolla hatchback 1.4 diesel (195 60 15 iirc).
Think the D4 are better on lighter and less powerful cars, A4s I would probably rate better for more powerful cars in the UK. Much depends on the size of wheel/tyre you want or need, they don't make both in all sizes!
The D4's pattern would make it more suitable if you encounter snow often - though couldn't say I had trouble with traction until I beached the car on a snow bank as I slowed down too much...
A4s are better in the dry and moist, wet they are about the same. My A4s have gotten a little bit noisy at 70-75mph, maybe because of asymmetric design? Not much worse than the Michelin Alpin A4 I had on before.