What do you like best?
OOP and component based deign of the framework (Write once, use eveywhere)
Ready-to-use components (e.g. wicket, wicket-jquery-ui and wicket-kendo-ui components)
Designing elegant architecture is simplified by the use of Java 8 and functional programming!
User guides and doccumentation.
Active releases and Apache support.
It is of course open-source, which helps you becoming master in Wicket.
Bean validation, Spring injection and Spring security integration.
Inherent protection against session fixation, request forgery, etc.
Having the liberty to push the load onto client or server.
What do you dislike?
Sometimes hacking with jquery-ui components can be daunting.
Sometimes you need to override an internal method, but realizing that it is a final method is just frustrating..
Java code in pages and components might get messy after some time.
You should search for the developer experiences and best practices for Wicket, before attempting to build a huge architecture...
Recommendations to others considering the product
Jump in the Wicket user guide and learn the basics. Build some simple pages at first. Then search for best practices before architecting an infrastructure. Wicket's internal working is very well documented. Read documents with full hearth, and see how the framework is designed. You will like it.
What business problems are you solving with the product? What benefits have you realized?
It's a real web framework. When you use Wicket, you theoretically and practically don't need any other library to use (yet, making use of jqery-ui integration makes you happy).
I think Wicket seems to be tailored for enterprise development, in which somebody needs to write a bunch of pages while the more experienced is developing the infrastructure...