It depends on what your software and hardware support requirements are. Windows 2003 Web Edition is really not made for running Active Directory and thus shouldn't really be in consideration. That leaves you with Windows 2003 Standard Edition, Windows 2003 Enterprise Edition and Windows 2003 Datacenter Edition. Windows 2003 Datacenter Edition is really made for mainframe type reliability and is typically sold for use in house large applications. As a result, it really doesn't fit the bill either. When it comes to the question of Windows 2003 Standard Edition or Windows 2003 Enterprise Edition, in my opinion the choice is simply a matter of your hardware requirements. Windows 2003 Standard Edition supports 4 GB RAM (partial support to 32 GB) and 4 way processing. Windows 2003 Enterprise Edition supports 64 GB RAM (partial support to 1 TB) and 8 way processing. In addition, Windows 2003 Enterprise Edition supports a number of additional pieces of functionality that Windows 2003 Standard Edition does not including:
- Identity Integration Feature Pack (IIFP)
- Terminal Server Session Directory
- Cluster Service
- Shadow Copy Transport
- Remote Storage
- Windows System Resource Manager (WSRM)
For a full breakdown of the product differences, check out Microsoft's Windows 2003 product information page.
In short, unless you need any of the additional hardware or feature requirements of Windows 2003 Enterprise Edition, I would recommend Windows 2003 Standard Edition. I would also recommend not performing an over the top upgrade of the system, but rather to install a new server to replace the old server, migrate the data and then decommission the old server. I've found that upgrading any previous operating system always seems to have negligible results when it comes to stability, and thus I try to avoid upgrading any critical systems if at all possible.