It is possible to install both versions but it will be counter productive sync your user defined settings from one to other.
Before you proceed further backup your settings. I am going to describe instructions for uninstalling Pycharm Community edition. You can also use this to remove Pycharm Professional edition.
Suppose you have pycharm Community installed at /home/<user>/ide/.
Use command this command rm -r ~/ide/pycharm-2016.3.2 to remove it.
You should also remove by these entries by using command rm -r. This contains your configs/license files for Pycharm.
rm -r ~/.PyCharm2016.3
rm ~/.gnome/apps/jetbrains-pycharm.desktop
rm -r ~/.java/.userPrefs/jetbrains/pycharm
rm ~/.local/share/applications/jetbrains-pycharm.desktop
Use sudo updatedb && locate pycharm to check whether other pycharm files are still left. If you any files that has pycharm in the name which is useful to you than don't delete them.
NOTE: If rm -r doesn't work use sudo rm -r.
/PycharmProjects. (Also, I had community and pro extracted to different directories.) – belacqua May 28 '14 at 23:45