John,
If you already have a plugin working with the C# client there is nothing to do, it's already supported by the current Web client 5.1 (and 5.5), with some limitations described in the doc: Using Legacy Script Plug-Ins with the vSphere Web Client
The Web Client SDK is for developing new UI (Flex) and server (Java) plugins with a much better integration with vSphere Web Client. It's a complete new API with a web architecture, your UI code will have to change but you can access your back-end the way you want. See that on-line doc or download the SDK and check out our samples and SDK doc.
