I need to constantly access a server to get real time data of financial instruments. The price is constantly changing so I need to request new prices every 0.5 seconds. The REST APIs of the brokers let me do this, however, I have noticed there's quite some delay when connecting to the server. I just noticed that they also have websocket API though. According to what I read, they both have some pros/cons. But for what I want to do and because speed is specially important here, which kind if API would you recommend? Is websocket really faster?
Thank you!
The most efficient operation for what you're describing would be to use a webSocket connection between client and server and have the server send updated price information directly to the client over the webSocket ONLY when the price changes by some meaningful amount or when some minimum amount of time has elapsed and the price has changed.  
This could be much more efficient than having the client constantly ask for new price changes and the timing of when the new information gets to the client can be more timely.
So, if you're interested in how quickly the information on a new price level gets to the client, a webSocket can get it there much more timely because the server can just send the new pricing information directly to the client the very moment it changes on the server.  Whereas using a REST call, the client has to poll on some fixed time interval and will only ever get new data at the point of their polling interval.
A webSocket can also be faster and easier on your networking infrastructure simply because fewer network operations are involved to simply send a packet over an already open webSocket connection versus creating a new connection for each REST/Ajax call, sending new data, then closing the connection.  How much of a difference/improvement this makes in your particular application would be something you'd have to measure to really know.
But, webSockets were designed to help with your specific scenario where a client wants to know (as close to real-time as practical) when something changes on the server so I would definitely think that it would be the preferred design pattern for this type of use.

Here's a comparison of the networking operations involved in sending a price change over an already open webSocket vs. making a REST call.
webSocket

Server sees that a price has changed and immediately sends a message to each client.
Client receives the message about new price.

Rest/Ajax

Client sets up a polling interval
Upon next polling interval trigger, client creates socket connection to server
Server receives request to open new socket
When connection is made with the server, client sends request for new pricing info to server
Server receives request for new pricing info and sends reply with new data (if any).
Client receives new pricing data
Client closes socket
Server receives socket close

As you can see there's a lot more going on in the Rest/Ajax call from a networking point of view because a new connection has to be established for every new call whereas the webSocket uses an already open call.  In addition, in the webSocket cases, the server just sends the client new data when new data is available - the client doens't have to regularly request it.
If the pricing information doesn't change super often, the REST/Ajax scenario will also frequently have "do-nothing" calls where the client requests an update, but there is no new data.  The webSocket case never has that wasteful case since the server just sends new data when it is available.
websocket vs rest API for real time data?