I would say Selenium standalone Server is good for several reasons:
It tests distribution over the remote machine, or multiple machines (nodes),
Selenium tests on different browsers with different versions,
Test that is not developed using the Java bindings (i.e. Python, C#, or Ruby) and would like to use HtmlUnit Driver
Selenium Client (jar) - It is as word say, a client, a bunch of API's rolled into one jar, for different languages (Ruby, Phyton, C#, Javascript etc.) So if You want to automate locally and test on the browser, one version of it, don't want to run in parallel, this is all You need. Client jar can also be acquired by tools like maven or Gradle, open-source build automation systems.
You should choose accordingly.
For more info visit https://intellipaat.com/blog/tutorial/selenium-tutorial/.
I am mentioning a video tutorial which I personally found very helpful. .