pgAdmin4 or pgAdmin3? I've seen a lot of hate directed to pgAdmin4, but honestly I can't see why. It worked out of the box from a docker image, connected right away to the database and perfectly managed every maintenance and query I've made.

Is there a good reason to keep using pgAdmin3?
Which database client to use is generally personal preference, and sometimes based on which client makes certain tasks the easiest to do.  

That said, pgAdmin3 doesn't connect cleanly to PG10+.  In that regard you will need to switch entirely to pgAdmin4 at some point.  If now is a convenient time then skip pgAdmin3.  

There are some obvious and non-obvious UX differences between the two, some features easier in pgAdmin3, some easier in pgAdmin4, but ultimately some users are just more comfortable with pgAdmin3.  How long you want to allow your fellow users/admins to use it is always dependent on your own use case.  I personally configured pgAdmin4 to use a browser that I don't normally use and that gives me a seperate location on my task bar to find my various query windows. This, and opening new query windows in new browser tabs have made pgAdmin4 more friendly for my own personal use. 

While discussing database clients, however, don't forget about psql.  The more I use it, the more I go to it first.  The -E command line option is a great learning tool for deciphering how the pg_catalog tables work and the \gexec internal command is extremely useful for as is \watch.