Well Dictionary, Webstorage are internal data storage. They are very similar except WS can save long term where as Dictionary is only session data. However both would be terrible for as long term data sources.
What you could do is use WebStorage and download your conversation trees by way of ajax on the first time the game is run. This is a good way to reduce the initial download size. However WS isn't really good for multi dimensional arrays. They are Key:Content only only 1 level.
Your best bet for creating a Dialog Conversation Tree would be to either
A. Stick to XML structure which XML is built for such things.
B. Right a plugin that takes advantage of a locally stored file to use your own structure or XML.
C. Built the conversation tree's internally :|
I have difficulties with XML myself, but it really is the best route to go for working with the system to it's best. If your trying to avoid manual coding. You could try looking for a plugin though. I think I have heard one mentioned around here and there.