I have read many posts on SO and the web regarding the keywords in my question title and learned a lot from them. Some of the questions I read are related to specific implem
HTTP limits the number of connections a client can have with a server to 2 (although this can be mitigated by using subdomains) and IE has been known to enforce this eagerly. Firefox and Chrome allow more (although I can't remember of the top of my head exactly how many). This might not seem like a huge issue but if you are using 1 connection constantly for real-time updates, all other requests have to bottleneck through the other HTTP connection. And there is the matter of having more open connections from clients puts more load on the server.
WebSockets are a TCP-based protocol and as such don't suffer from this HTTP-level connection limit (but, of course, browser support is not uniform).