Disclaimer: I'm not aware of particularities of TomEE configuration. However, you should consider them as completely separate entities and ignore their common ancestry. As you correctly write, they're both separate binaries, further more they might change at different times when upgraded, and thus the demand to configure them to access the same directory does not make any sense. Also, TomEE contains a lot of additional common libraries in its lib
directory - do you really want to share them with your Tomcat installation?
Just because they (might) honor an environment variable with the same name does not make them magically work with whatever they find there. With the same reasoning, you might want to claim to run tomcat 7, 8.5 and 9 to run from the same home directory - they honor the same CATALINA_HOME variable as well - and here it might be clearly visible that there's not a chance that they'll all work together.
Also, you don't need to worry about changing CATALINA_HOME when starting: Tomcat will figure out its CATALINA_HOME automatically if you don't set it, so the whole problem is already solved without doing anything.