After two days of trying I finally got it to work on Tomcat.
Apperantly Tomcat does not support JAXWS-RI by default, which was needed, so I had to switch my JAXWS libraries by JAXWS-RI libraries.
Then on Tomcat I had to add the "endorsed" directory to the Tomcat home directory and place jaxws-api.jar (from JAXWS-RI) in there otherwise it conflicted with Tomcats own classes.
Hopefully someone else will find this useful in the future!