Full disclosure: I work for Kaazing and I have not used jWebSocket myself.
A couple of quick points:
0) Production vs. Beta
Kaazing is production-quality software. The download link on the jWebSocket web page points me to a beta version of the product.
1) Client Technologies
Kaazing provides WebSocket libraries for multiple client technologies (JavaScript, Java, .NET/Silverlight, and Flash), It looks like jWebSocket provides JavaScript and Java. You mention you would need a Flash client and AFAIK only Kaazing provides that. jWebSocket uses Flash for emulation (see the next point).
Note: Kaazing now provides AngularJS, ReactJS, Objective-C (iOS), Xamarin (.NET with support for iOS and Android), Java, .NET, and Android clients. However support for SilverLight and Flash have been deprecated.
2) Emulation (for browsers that do not support WebSocket)
jWebSocket requires Flash, Kaazing does not.
Note that Flash emulation for secure WebSocket (wss://) requires you to open a separate port for the Flash x-domain policy file. In many enterprises this is a non-starter.
3) Protocol Support
Kaazing offers a wide range of higher-level protocols on top of WebSocket: JMS (can run against any back-end JMS message broker), STOMP, AMQP, XMPP, etc. I don't know what jWebSocket does in this space.
4) Enterprise Deployment
It is easy to configure the Kaazing WebSocket Gateway in conjunction with existing Directory services (LDAP). It supports Single Sign-On, and the gateway can easily be clustered for HA purposes (again, not quite sure what jWebSocket does here.)
Please take a look at the documentation for these features:
Security configuration:
5) Open Source
jWebSocket is open source, Kaazing has both an open source Community Edition and an Enterprise Edition.
Hope this helps for now!