WebSockets are a bidirectional data exchange within a HTTP connection. So the question is not if you use HTTP or WebSockets, because there is no WebSockets without HTTP. WebSockets are often confused with simple (BSD) sockets, but WebSockets are actually a socket-like layer inside a HTTP connection which is inside a TCP connection which uses "real" sockets. Or for anybody familiar with OSI layers: it as a layer 4 (transport) encapsulated inside layer 7 (application) and the main reason for doing it this strange way instead of using layer 4 directly is that plain sockets to ports outside of HTTP, SMTP and a few other protocols are no longer possible because of all the port blocking firewalls.
So the question should be more if you use simple HTTP or if you need to use WebSockets (inside HTTP).
- With simple HTTP the client sends a request and the server sends the response back. The format is well defined and browser and server transparently support compression, caching and other optimizations. But this simple request-response pattern is limited, because there is no way to push data from server to client or to have a more (BSD) socket like behavior where both client and server can send any data at any time. There are various more or less good workarounds for this, like long polling.
- WebSockets gives you a bidirectional communication, which makes it possible for the server to push data to the client or to send data in both directions at any time. And once the WebSocket connection is established by upgrading an existing HTTP connection the overhead for the data itself is very small, much smaller then with a full new HTTP request. While this sounds good you loose all the advantages of simple request-response HTTP like caching at the client or in proxies. And because client and server need resources to keep the underlying TCP connection open it needs more resources, which can be relevant for a busy server. Also, WebSockets might give you more trouble with middleboxes (like proxies or firewalls) then simple HTTP does.
In summary: if you don't need the advantages of WebSockets stay with simple request-response HTTP.