I have deployed web-apps designed for Tomcat on GlassFish. Have you tried to use the GlassFish admin console to deploy it as a Web Application ? Do you package all the dependencies (Spring frameworks, hibernate) in the web-app .war file when you deploy on Tomcat? If some things are not included in the .war file, you may want to include them in <GlassFish installdir>/lib. I have seen other directories recommended for this purpose, as well, but this one generally works.
Some of the Tomcat based web-apps I have seen also have had configuration files that assume the application is deployed in the Tomcat webapp directory and you need to take into consideration that this will be different in GlassFish
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