I've been searching and reading up on SignalR recently and, while I see a lot of explanation of what the difference is between Hubs and Persistent Connections I haven't been able to get my head around the next level, which is why would I choose one approach over the other?
From what I see in the Connection and Hubs section it seems that Hubs provide a topic system overlaying the lower-level persistent connections.
From the highly up-voted comment below:
Partially correct. You can get topics or groups in persistent connections as well. The big difference is dispatching different types of messages. For example you have different kinds of messages and you want to send different kinds of payloads. With persistent connections you have to embed the message type in the payload (see Raw sample) but hubs gives you the ability to do RPC over a connection (lets you call methods on on the client from the server and from the server to the client). Another big thing is model binding. Hubs allow you to pass strongly typed parameters to methods.
The example used in the documentation uses a chat room metaphor, where users can join a specific room and then only get messages from other users in the same room. More generically your code subscribes to a topic and then get just messages published to that topic. With the persistent connections you'd get all messages.
You could easily build your own topic system on top of the persistent connections, but in this case the SignalR team did the work for you already.