Same problem with Xubuntu 16.04.1 LTS, fully updated (gnome-software 3.20.1+git20160617.1.0440874.ubuntu-xenial-0ubuntu1~16.04.1).
Launching gnome-software with terminal does nothing.
Removing the ~/.local/share/gnome-software/ worked as workaround.
Same problem with Xubuntu 16.04.1 LTS, fully updated (gnome-software 3.20.1+ git20160617. 1.0440874. ubuntu- xenial- 0ubuntu1~ 16.04.1) .
Launching gnome-software with terminal does nothing.
Removing the ~/.local/ share/gnome- software/ worked as workaround.