There seems to be a lot of confusion when it comes to what's the difference, which is better, etc., so I wanted to provide you with some of the basics - not my intention to get into the gritty details as I believe in casting a wide net on this subject is more beneficial.
First, both knives offer you a supreme investment in your kitchen. They will last you for decades, even a lifetime or two if cared for properly. Both types give the strength of a full-tang, which means the blade runs all the way to the handle of the knife, which aids in ease of cutting whatever you are trying to cut.
Why are there differences in a brand price-wise if the blade is all the same? Well, it's the handle basically - even different composite handles, design aesthetics contribute to the overall cost of a knife. Believe it or not, various types of resin cost different prices - wood handles tend to cost more.
For the most part, all European/German knives offer you the same blade - the steel from which it is forged is fairly similar, with very little variance between them all. I tell people it comes down to how does the knife feel in your hand, because ultimately that comfort is what is going to determine your satisfaction of the overall experience - aside from the knife actually cutting something well. Women tend to prefer small-scale handles, men larger - not a surprise there.
Blades differ greatly between the two camps as European knives use a softer steel which from an overall lifestyle perspective applies to most households where knives are dropped. The softer metal bounces back so to speak, where the harder, Asian metal is more brittle and will break or chip much easier. A softer metal will require more sharpening, whereas the harder metal stays sharper longer. European blades tend to be thicker for this reason and Asian knives, due to their hardness will be thinner and more stealth-like.
The wave effect you sell on Asian knives is a technique where the metals are bonded together through a hammering process that can constitute 100-200 layers of bonded alloy to create a superior blade that will be sharp 20 times longer than your European knife - yet you will pay for the strength as well.
European manufacturers have been making Asian-style knives for years, i.e. the Santoku blade, which is a flat-ish bladed knife with inverted divets all along the bottom edge which allows the user to slice foods thinly with less sticking. The divets allow for air flow - less stickability, so to speak. The flat surface is intended for up and down chopping, not rocking such as a chef's knife which is angled. Most American's have been taught to use a rocking motion when cutting their food.
Asian manufacturers do have several European-style knives, yet you will notice that the blade as less of an upward angle since Asian knives are made in a manner to have more contact with the cutting surface, allowing the user to cut more product at once, faster.
Where to buy
European - Wusthof, www.Wusthof.com
Asian - Zwilling/Bob Kramer, www.ZwillingOnline.com