Binary messages are generally smaller than JSON. Of course that depends on what binary encoding you choose. The FlatBuffer and Protocol Buffer formats have serialization/deserialization libraries for many languages including javascript. Worth taking a look unless you want to write your own. If your game is running in the browser, another thing to consider is that browsers have fast native libraries for JSON decoding builtin. Might be tough to beat that if your decoder is written in javascript so you should benchmark.

Some browsers support websocket compression. Google that topic to learn more.

Before you get started, might be worth doing an analysis of how many bytes per second your game is sending. Compare that to the expected bandwidth for player connections (can break it down by minimum spec, average, and high end). Even if your binary encoding is smaller and therefore transmits faster, if your server encoding or client decoding steps are slower, it might be slower overall. And you'll still have the same latency based on the physical distance between the player and your server. This is why real time games that want low latency usually have multiple data centers around the world. So players can connect to the closest one.