It seems that JEE applications no longer need the use of a complex application server like WAS 9 and are deployed on a simple tomcat. Is it true? What is the trend today?

Do you need car or train to go to your work? Or maybe bicycle will be enough, or you could just walk - so it depends - from distance, traffic, etc.

Same is with app and servers - depends on what features you really need. Of course you can use Tomcat and pack 100MB of third party jars in that, but why do that??

If you are unsure - just use WebSphere Liberty, where you can select what features will be loaded. It can be as lightweight as Tomacat, but also full featured as Java EE server.

It depends on what your business needs.  You can start with Liberty, or ICP - IBM Cloud Private. 

https://www.ibm.com/blogs/bluemix/2016/05/websphere-liberty-different-from-traditional-was-p2/

ftp://public.dhe.ibm.com/software/webservers/appserv/was/pdf/WebSphereApplicationServer_CompareEditions_v6.pdf

As Michael said, it really depends on the application.

For new applications I would for sure start with WebSphere Liberty - or even with the Open Source Version which is Open Liberty (openliberty.io). For older applications I would try to go to Liberty if possible.

From my experience in the field, there are only three main reasons why people stick with WAS Traditional

- they use wsadmin scripting and do not have a deployment tool which could be used with Liberty instead

- they have a very old application which relies on older standards and cannot be migrated

- they need something like remote EJB workload management which is not available in Liberty