GUI Firefox, Safari and other apps freeze after 10.11.3 update
I'd start with the standard 'troubleshooting toolkit'..


Fix permissions, Verify &amp; if necessary Repair disk, using Disk Utility.
Reset Home folder permissions &amp; ACLs using OnyX  - Maintenance tab/permissions, tick the box at the top then Execute. (Make sure you get the right version for your OS.)
Reset the SMC (instructions depend on Mac model)
Reset the NVRAM


At the boot chimes, hold  Cmd ⌘   Opt ⌥   P   R  
Keep holding all 4 keys until you hear the chimes again, then release

Start in Safe Mode 


Start or restart your Mac. 
Immediately after you hear the startup sound, press and hold the Shift key.
Release the Shift key when you see the Apple logo appear on the screen.
Leave a few minutes after login for caches to rebuild, then reboot normally.

Update to 10.9.5 using the 10.9.5 combo update, not the delta from App Store