Pros and Cons of accessing SQL management studio via server installs vs local installs

I've been looking around to see if I can find some opinions on accessing SQL management studio directly via the server it is installed on(where the databases are) vs installing a local copy to a desktop and then logging into the databases via object explorer.
I've worked in different places that use different options, and I assumed the reasons are largely based on the clients preference/hosting of servers. However I wondered if there were any actual pros and cons around the two different options that can make one preferable;
ie. is one a more secure option? Are certain things impossible to set up locally?

I find object explorer very convenient for switching between databases and servers, and being able to set things up as registered servers more so.
Obviously if there is anything outside of SQL that requires server access I still have to log on so it may not always be quicker, but I'm interested in hearing what others think.