11.7 is the last release in which the "Classic" App Server is available. After that, only the Tomcat-based PASOE is available.
There is certainly a learning curve with PASOE but it is the future. My advice is to embrace it as soon as you can; it's not as if App Server is going to make a comeback.
Migrating existing App Server-based applications to it isn't too difficult. We've migrated our App Server-based web services to PAS.
PAS gives several benefits from being Tomcat-based. It uses the Spring security framework, it can be used with third-party Tomcat load balancers, and there is information available online on best practices for configuration, hardening, etc., and you will be able to find people in the job market with Tomcat experience (much more readily than finding people with App Server experience). It also ships with web apps that help you inspect the health of, manage, and monitor your PAS instances and apps.
Most importantly, it will grow and improve over time as PSC invests in new features, better performance, reliability, security, and bug fixes. App Server is frozen in time. It will never improve and when you inevitably upgrade to 12.x you'll have to leave it anyway. Yes, there will be bumps along that road but you have to travel on it eventually. Might as well get the bumps behind you sooner rather than later.