Hello Pieter,
dropping JARs in tomcat/shared/lib requires that the catalina.properties file in tomcat/conf lists a pattern of ${catalina.base}/shared/lib/*.jar in its shared.loader configuration. Depending on how you've installed Alfresco, this may not be set by default. I think ${catalina.base}/shared/*.jar is the default.
Proper AMP files can in fact be uninstalled using the Module Management Tool (Alfresco MMT). The success of this though relies upon a non-conflicting installation history, e.g. the module did not override a file during installation that another module later overrode again later on.
Dropping in JAR files is usually safer and quicker (and easier to comprehend), but the standard advice to drop it into tomcat/shared/lib has only limited validity. That can only work if the JAR itself has no direct dependencies on Alfresco. In other cases, those JAR files need to be dropped into tomcat/webapps/alfresco/WEB-INF/lib or tomcat/webapps/shared/WEB-INF/lib.
Once you remove a JAR from the folder and restart, all the configuration changes and extra code it introduced are gone. But if it did bootstrap some configuration / code as content into the Data Dictionary, that will remain and may need to manually removed.
Regards
Axel