I understand the difference in general terms, it is for synching and sharing data across client and server.

But for my own registry, which would be better to use and why?

If possible could I have some use cases for each.

It's the other way around we would need to know what you're planning to tell you the benifits. However simple answer is Forge registries do all the hard work of saving/loading/syncing/substitutes/aliases/networking for you. So if you use any of those features it's probably best to use ours. But if you're working internally and don't need numerical ids for networking or dynamic substitutions then a normal map would work.

My use is holding a map of classess for an RPG style mod, with the potential for other mods to add classes. The classes are required on both sides, but will be set via a GUI. How should I go about syncing the data, I am currently sending the ResourceLocation of the class as a string in my packets.