As far as I understand, Visual Web Developer (VWD) is simply a free version of the Visual Studio components necessary to develop web based solutions.
Here is a list of features missing from VWD that you get in a Professional edition of Visual Studio 2008 (VS2008). In short, VWD Express 2005
is Not Extensibile with other add-ons or third party tools
Only supports Web site projects (2005). You cannot add a Class
Library project or a Web Controls
Library project to the solution.
UPDATED - VWD 2008 SP1 also allows Web Application and Class Library Projects in the solution.
Lacks the ability to combine Source Code Control
has no Accessibility checker
Lacks ability for automatic generation of resources for
localization
Cannot attach debugger to a process
has no Native code debugging
The obvious advantage of VWD over VS2008 is that it is free and if you can work smart with it given the missing features, it may be the more pragmatic option for you. If those are features that you can't live without, VS2008 may be a wise investment - you also get all of the features missing from other Express products (Visual Basic 2008, Visual C# 2008, etc).
Take a look at MSDN's comparison chart for Visual Studio 2005. I can't find 2008's but would suspect it to be very similar.