Though neither of these knives are personal favorites, they are both brilliant pieces of cutlery and deserve a tip of the hat. Given the choice between them, I would be able to pick a clear favorite, however. Since I prefer lighter knives with more ergonomic handles, I deeply prefer the Shun Premier. That being said, anyone liking a classic French knife would love the Wusthof Classic.
The Shun Premier is a classic Japanese style chef's knife. It's thin, light, and elegantly designed. I love its hammered Damascus steel, which makes it look like a samurai artifact. The combination of steels used in the blade construction gives it a nice balance of a hard high-carbon core and a softer Damascus steel coating and protecting the brittle interior. It's not a knife well suited to heavy-duty tasks, however, so some finesse is required to use it to its full effect.
The Wusthof Classic line of knives is no less impressive. It's heavier, sturdier, and has the shape of handle that most Western chefs have grown accustomed to. It's forged high-carbon stainless steel is strong, durable, and can take an edge with a minimum of maintenance. The edge is precision engineered with Wusthof's patented PETec process. It also has a thick bolster and fingerguard supporting the heel of the knife, which along with its weight makes it a great heavy-duty knife. It may be a little heavy for some, though, and I've never been a fan of the typically blocky European knife handles.
The Wusthof Classic line tends to have a smooth blade (though there is a dimpled or hollow ground version). This flat blade makes slicing thinly a little trickier as food sticks to the flat of the blade. The Shun Premier's blade catches little pockets of air under the slices and makes it much easier to slice food extremely thin. It is a bit more prone to having little bits of food stuck inside, but the hammered look is just so pretty I'm going to forgive it for being a little less convenient.
In the typical Japanese style, the bolster only serves to connect the handle to the blade and is about as thick as the thinnest section of handle. It's light because the blade is light and it doesn't have to balance it out so much. I like light knives. On the other side, though, there's a lot to be said about a big, beefy bolster. The Wusthof has a reinforced bolster and fingerguard that also makes the heel into a perfect wedging and cracking tool. Though I keep a big, heavy, cheap knife for such things, it does make the Wusthof more versatile and robust.
It's look at the obvious time. The handles of these two knives are drastically different, and on first glance the Wusthof seems to have a more ergonomic design. Unfortunately, it's also blocky and square in profile. I don't find these knives especially comfortable or easy to get a good grip on. The Shun Premier has a rounded handle that from the side looks straight, but actually fits into the naturally rounded grip of your hand much better (I think) without too much strength necessary. Another point for Shun.
Generally, I'm a fan of high-carbon stainless steel like the Wusthof Classic is made of. The reason for that, though, is that high-carbon steel is just such a pain to maintain. It requires so much effort and attention to keep it from discoloring or chipping. The Shun deals with that nicely with it 16 layers of Damascus steel protecting the business end of the blade. These knives take a wicked edge, but the edge itself can be a brittle so it's important to respect it.
The Wusthof Classic is perfect for classically European influenced chefs. It's deeply familiar and a top quality tool. Strictly as a matter of personal aesthetic and comfort preferences, however, it's not my favorite of the two.
The Shun premier is a classic Japanese style knife, and a clear choice for anyone coming from the Japanese cooking tradition. It's also lighter, has a comfier handle, and it's aesthetics approach art. Definitely my favorite in this duo.
If these knives are a bit old-school and stuffy for your tastes, though, check out the comparison of the Global G-2 and Shun Ken Onion. Those are two knives that push the modern envelope very nicely.