My Droid Maxx updated on June 4th and ever since it has been a sluggish. The persistent symptom is that I click something and it just hangs. Sometimes it is the start of an app, sometimes it is just a letter on the keyboard. The phone just periodically spaces out.
I have cleared apps, seen to it that the free RAM memory and storage is plentiful so it's not memory.
I imagine it may be app conflicts. You can uninstall apps one by one, or (my personal option) backup your files, and disable app backup, then factory reset your phone.