The current version of APM Local Client (ver. 9.51) has a lot of restrictions compared to the browser based APM GUI:
Only one tab
In "normal" web browsers (IE, Firefox) you can open several tabs to work in different sections of APM. Launching several instances of Local Client is only a poor workaround.
Launch of new Windows
Some (admin) UIs (e.g. EUM Monitoring Adminstration) will be opened in a new Window outside the Local Client Window. The Local Client Window remains blank.
BPM Admin UI
Launching the BPM Admin UI from Local Client (Admin -> EUM -> Settings) opens the default browser of the system you are working on. So a Java plugin is required for this browser again as the BPM UI is still a java applet. The purpose of the "Local Client" is to replace the Java Plugin in the browser.