For the uninitiated, Shockwave movies are created with Macromedia Director, which is an authoring tool with a pedigree reaching back to the mid-1980's. Flash movies are created with Macromedia Flash, which came into being around 1997. Both tools are popular for creating content that appears in web-pages. Flash is more popular and is used in everything from web-ads to games to cellphones nowadays.
That being said, IMHO Shockwave still has three advantages over Flash:
1. You've got pixel-level control of the graphics on your screen. Flash just works with lists of curves or objects made of collections of curves. Flash does bitmaps okay, but only as immutable objects. You can't mess with the pixels in your Flash movie. Period.
2. Shockwave has a 3D engine. While it's not been updated in a few years and has pretty-much "hit the wall" as to the quality of content you can make with it, Shockwave's still got more 3D than Flash (i.e. more than zero).
3. Shockwave is extensible. Shockwave's got the concept of an "Xtra", which is a DLL-ish piece of code written in machine code (i.e. in C++) so you can have system-level control. That way if you write a program that needs to "break out of the sandbox" and do stuff that standalone apps require, like talking to the registry or reading and writing files, you can do it. Macromedia's got a "blessed" xtras program to help prevent people from writing malicious stuff.
Even though the new Flash 8 development environment is still a couple of months away, people have been hacking furiously at the new beta player. And those hackers found that you've now got access to the pixels.
Here's a cool page with some hacked-together demos of pixel-fiddling. You'll need the Flash 8 player to view these demos. They show off some techniques that'd be impossible with earlier versions of Flash.
That leaves 3D and Xtras. If you're making a standalone double-clickable Flash application, there are a few third-party solutions that'll let you extend your Flash app with native code. There's still no method to do it in an embedded web-app, but I don't know if that's a big enough need yet. So that's still about half of an advantage.
3D's still not there and isn't, far as I know, on the horizon.
That leaves 1.5 advantages that Shockwave's still got, and I don't think that's enough to overcome its lower browser-penetration. Expect Shockwave to either be bought out by another company or follow the PageMaker route of ongoing maintenance for the fans but no further big updates.