Here is a breakdown of the differences between the various Windows Server 2003 editions. This information is from the Parameg site – I decided to include it due to it’s nice clear explanations.
Windows Server 2003 Web Edition
Windows Server 2003, Web Edition is mainly for building and hosting Web applications, Web pages, and XML Web Services. It is designed to be used primarily as an IIS 6.0 Web server and provides a platform for rapidly developing and deploying XML Web services and applications that use ASP.NET technology, a key part of the .NET Framework. This edition does not require Client Access Licenses and Terminal Server mode is not included on Web Edition. However, Remote Desktop for Administration is available on Windows Server 2003, Web Edition. Only 10 concurrent file-sharing connections are allowed at any moment. It is not possible to install Microsoft SQL Server and Microsoft Exchange software on this version of Windows, although MSDE and SQL Server 2005 Express are fully supported after service pack 1 is installed. The most important limitation of Web edition is a maximum memory of 2 GB RAM. Additionally, Windows Server 2003, Web Edition cannot act as a domain controller. See Compare the Editions of Windows Server 2003.
Windows Server 2003 Standard Edition
Windows Server 2003, Standard Edition is aimed towards small to medium sized businesses. Flexible yet versatile, Standard Edition supports file and printer sharing, offers secure Internet connectivity, and allows centralized desktop application deployment. This edition of Windows will run on up to 4 processors with up to 4 GB RAM. 64-bit versions are also available for the AMD x86-64 architecture and the Intel clone of that same architecture, EM64T. The 64-bit version of Windows Server 2003, Standard Edition is capable of addressing up to 32 GB of RAM and it also supports Non-Uniform Memory Access (NUMA), something the 32-bit version does not.
Windows Server 2003 Enterprise Edition
Windows Server 2003, Enterprise Edition is aimed towards medium to large businesses. It is a full-function server operating system that supports up to eight processors and provides enterprise-class features such as eight-node clustering using Microsoft Cluster Server (MSCS) software and support for up to 32 GB of memory. Enterprise Edition also comes in a 64-bit edition for Intel. 64-bit versions are also available for the AMD x86-64 architecture and the Intel clone of that same architecture, EM64T. The 64-bit version of Windows Server 2003, Enterprise Edition is capable of addressing up to 1 TB of RAM. Both 32-bit and 64-bit versions support Non-Uniform Memory Access (NUMA).
Windows Server 2003 Datacenter Edition
Windows Server 2003, Datacenter Edition is the flagship of the Windows Server line and designed for immense infrastructures demanding high security and reliability. Datacenter supports up to 64 processors. It also supports Non-Uniform Memory Access (NUMA).
Windows Server 2003 Compute Cluster Edition
Windows Server 2003, Compute Cluster Edition is designed for working with the most difficult computing problems that would require high performance computing clusters. Compute Cluster edition deploys in clusters of multiple servers to form large supercomputers. Microsoft intends to release this edition in 2006.
Windows Server 2003 Storage Server
Windows Storage Server 2003 is optimised to provide dedicated file and print sharing services. It is only available through OEMs when purchased pre-configured with network attached storage devices, which are available in a wide variety of sizes from a couple hundred gigabytes to a few terabytes. One significant difference, when compared with the other Windows Server 2003 editions that provide file and print services, is that Storage Server does not require client access licenses.
Also, here is a good Microsoft TechNet library article that clearly outlines the differences between the versions of Windows Server 2003.
This Microsoft article also offers similar information.